Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1348 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C4×C13×C22⋊C4 | C2 |
| hypercenter | C4×C22⋊C4 | D13 |
| hypocenter | C13 | #2433 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D52 | C2 | semidirect |
| 2. C2×#88184 | C2 | semidirect |
| 3. C2×#88136 | C2 | semidirect |
| 4. C2×#88128 | C2 | semidirect |
| 5. C4×C13×C22⋊C4 | C2 | semidirect |
| 6. #11718600 | C2 | semidirect |
| 7. #11718332 | C2 | semidirect |
| 15. C22×D52 | C22 | semidirect |
| 16. C22×D52 | C22 | semidirect |
| 18. C2×C42×C13 | C22 | semidirect |
| 20. C2×#6103 | C22 | semidirect |
| 21. C2×#6103 | C22 | semidirect |
| 22. C2×C4⋊Dic13 | C22 | semidirect |
| 25. C13×#95 | C22 | semidirect |
| 34. C22×C4×C13 | D4 | semidirect |
| 51. C2×D52 | D4 | semidirect |
| 52. C13×C22⋊C4 | D4 | semidirect |
| 83. C2×C4×C13 | C2×D4 | semidirect |
| 97. C4×C22⋊C4 | D13 | semidirect |
| 101. C22×C13 | #127 | semidirect |
| 118. C4×C13 | #120 | semidirect |
| 136. C2×C42 | C2×D13 | semidirect |
| 137. #95 | C2×D13 | semidirect |
| 167. C22×C4 | D52 | semidirect |
| 174. C22⋊C4 | D52 | semidirect |
| 176. C13 | #2433 | semidirect |
| 208. C2×C4 | C2×D52 | semidirect |
| 223. C22 | #88128 | semidirect |
| 231. C4 | #88136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C2×#88184 | 2 |
| C2×#88136 | 2 |
| C2×#88128 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718600 | 2 |
| #11718332 | 2 |
| #2433 | 13 |