Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C13×#376 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C22×D52 | C22 |
| hypercenter | #376 | D13 |
| hypocenter | C13 | #2372 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#376 | C2 | semidirect |
| 3. #11718601 | C2 | semidirect |
| 4. C4×#6103 | C2 | semidirect |
| 5. #11718593 | C2 | semidirect |
| 6. #11718330 | C2 | semidirect |
| 7. #11718327 | C2 | semidirect |
| 9. #11718307 | C2 | semidirect |
| 23. #88129 | C4 | semidirect |
| 49. C2×Dic26 | C2×C4 | semidirect |
| 51. C42×C13 | C2×C4 | semidirect |
| 55. #6103 | C2×C4 | semidirect |
| 56. #6103 | C2×C4 | semidirect |
| 102. #376 | D13 | semidirect |
| 178. C42 | C4×D13 | semidirect |
| 179. C13 | #2372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88129 | 2 |
| C13×#376 | 2 |
| #11718601 | 2 |
| C4×#6103 | 2 |
| #11718593 | 2 |
| #11718330 | 2 |
| #11718327 | 2 |
| #11718326 | 2 |
| #11718307 | 2 |
| #2372 | 13 |