Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
620 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 181 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×#384 | C2 |
| prime radical | C22×D52 | C22 |
| hypercenter | #384 | D13 |
| hypocenter | C13 | #2538 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88151 | C2 | semidirect |
| 3. C2×C4×Dic26 | C2 | semidirect |
| 4. C13×#384 | C2 | semidirect |
| 5. #11718655 | C2 | semidirect |
| 7. #11718648 | C2 | semidirect |
| 8. #11718646 | C2 | semidirect |
| 38. C2×D52 | Q8 | semidirect |
| 44. C2×Dic26 | D4 | semidirect |
| 96. #384 | D13 | semidirect |
| 115. C4×C13 | C22⋊Q8 | semidirect |
| 175. C13 | #2538 | semidirect |
| 228. C4 | #88151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88151 | 2 |
| C2×C4×D52 | 2 |
| C2×C4×Dic26 | 2 |
| C13×#384 | 2 |
| #11718655 | 2 |
| #11718649 | 2 |
| #11718648 | 2 |
| #11718646 | 2 |
| #2538 | 13 |