Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
576 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 576 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 | C22×C13 | C23×C4 |
| Fitting, prime radical | C2×C13×#121 | C2 |
| socle, cosocle | C23×C13 | C24 |
| hypercenter | C2×#121 | D13 |
| hypocenter | C13 | #2377 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11718882 | C2 | semidirect |
| 3. #11718881 | C2 | semidirect |
| 4. #11718881 | C2 | semidirect |
| 5. #11718873 | C2 | semidirect |
| 6. #11718872 | C2 | semidirect |
| 7. #11718642 | C2 | semidirect |
| 8. #11718612 | C2 | semidirect |
| 9. #11718611 | C2 | semidirect |
| 14. C13×#121 | C4 | semidirect |
| 38. C2×D4×C13 | C2×C4 | semidirect |
| 40. C22×C4×C13 | C2×C4 | semidirect |
| 51. C13×C4⋊C4 | C2×C4 | semidirect |
| 52. C13×C22⋊C4 | C2×C4 | semidirect |
| 136. #121 | Dic13 | semidirect |
| 167. C2×D4 | C2×Dic13 | semidirect |
| 176. C22×C4 | C2×Dic13 | semidirect |
| 182. C4⋊C4 | C2×Dic13 | semidirect |
| 189. C22⋊C4 | C2×Dic13 | semidirect |
| 191. C13 | #2377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#121 | 2 |
| #11718882 | 2 |
| #11718881 | 2 |
| #11718873 | 2 |
| #11718872 | 2 |
| #11718642 | 2 |
| #11718612 | 2 |
| #11718611 | 2 |
| #2377 | 13 |