Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1224 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 201 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 | C13×#380 | C2 |
| hypercenter | #380 | D13 |
| hypocenter | C13 | #2847 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×D13 | C2 | semidirect |
| 2. C2×#88184 | C2 | semidirect |
| 3. C2×#88149 | C2 | semidirect |
| 4. C2×#88136 | C2 | semidirect |
| 5. C13×#380 | C2 | semidirect |
| 6. #11718648 | C2 | semidirect |
| 7. #11718619 | C2 | semidirect |
| 8. #11718326 | C2 | semidirect |
| 14. C22×D52 | C22 | semidirect |
| 19. C2×C13×C4⋊C4 | C22 | semidirect |
| 23. C2×#6103 | C22 | semidirect |
| 24. C2×#6103 | C22 | semidirect |
| 25. C2×C4⋊Dic13 | C22 | semidirect |
| 28. C13×#95 | C22 | semidirect |
| 29. #88071 | C22 | semidirect |
| 35. C23×D13 | D4 | semidirect |
| 39. C22×C4×C13 | D4 | semidirect |
| 61. C2×C4×D13 | D4 | semidirect |
| 119. #380 | D13 | semidirect |
| 124. C22×C13 | #121 | semidirect |
| 142. C2×D13 | #121 | semidirect |
| 145. C4×C13 | #120 | semidirect |
| 162. C2×C4⋊C4 | C2×D13 | semidirect |
| 168. #95 | C2×D13 | semidirect |
| 205. C22×C4 | D52 | semidirect |
| 215. C13 | #2847 | semidirect |
| 276. C22 | #88149 | semidirect |
| 286. C4 | #88136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D13 | 2 |
| C2×#88184 | 2 |
| C2×#88149 | 2 |
| C2×#88136 | 2 |
| C13×#380 | 2 |
| #11718648 | 2 |
| #11718619 | 2 |
| #11718326 | 2 |
| #2847 | 13 |