Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C17×#400 | C2 |
| hypercenter | #400 | D17 |
| hypocenter | C17 | #2828 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11762738 | C2 | semidirect |
| 2. #11762727 | C2 | semidirect |
| 3. #11762726 | C2 | semidirect |
| 4. #11762726 | C2 | semidirect |
| 5. #11762719 | C2 | semidirect |
| 6. #11762719 | C2 | semidirect |
| 7. #11762710 | C2 | semidirect |
| 8. #11762698 | C2 | semidirect |
| 9. C17×#400 | C2 | semidirect |
| 128. #400 | D17 | semidirect |
| 165. C17 | #2828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762738 | 2 |
| #11762727 | 2 |
| #11762726 | 2 |
| #11762719 | 2 |
| #11762710 | 2 |
| #11762698 | 2 |
| C17×#400 | 2 |
| #2828 | 17 |