Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1348 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 197 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 | C2×C13×#121 | C2 |
| hypercenter | C2×#121 | D13 |
| hypocenter | C13 | #2433 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D52 | C2 | semidirect |
| 2. C2×C13×#121 | C2 | semidirect |
| 3. C2×#88194 | C2 | semidirect |
| 4. C2×#88191 | C2 | semidirect |
| 5. C4×C22⋊Dic13 | C2 | semidirect |
| 6. #11718649 | C2 | semidirect |
| 7. #11718621 | C2 | semidirect |
| 10. C22×D4×C13 | C22 | semidirect |
| 12. C22×C22⋊D13 | C22 | semidirect |
| 18. C2×C13×C4⋊C4 | C22 | semidirect |
| 19. C2×C13×C22⋊C4 | C22 | semidirect |
| 23. C2×#6103 | C22 | semidirect |
| 24. C2×C4×Dic13 | C22 | semidirect |
| 25. #88071 | C22 | semidirect |
| 38. C22×C4×C13 | D4 | semidirect |
| 51. C2×D52 | D4 | semidirect |
| 54. C22⋊Dic13 | D4 | semidirect |
| 88. C2×Dic13 | C2×D4 | semidirect |
| 93. C2×#121 | D13 | semidirect |
| 105. C22×C13 | #127 | semidirect |
| 118. C4×C13 | #120 | semidirect |
| 127. C22×D4 | C2×D13 | semidirect |
| 132. C2×C4⋊C4 | C2×D13 | semidirect |
| 135. C2×C22⋊C4 | C2×D13 | semidirect |
| 167. C22×C4 | C22⋊D13 | semidirect |
| 176. C13 | #2433 | semidirect |
| 223. C22 | #88194 | semidirect |
| 231. C4 | #88191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C2×C13×#121 | 2 |
| C2×#88194 | 2 |
| C2×#88191 | 2 |
| C4×C22⋊Dic13 | 2 |
| #11718649 | 2 |
| #11718621 | 2 |
| #2433 | 13 |