Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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×#390 | C2 |
| prime radical | C22×D4×C17 | C22 |
| hypercenter | #390 | D17 |
| hypocenter | C17 | #2808 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11762734 | C2 | semidirect |
| 3. #11762721 | C2 | semidirect |
| 4. #11762715 | C2 | semidirect |
| 5. #11762707 | C2 | semidirect |
| 6. #11762702 | C2 | semidirect |
| 7. #11762702 | C2 | semidirect |
| 8. #11762690 | C2 | semidirect |
| 154. C17 | #2808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762734 | 2 |
| #11762723 | 2 |
| #11762721 | 2 |
| #11762715 | 2 |
| #11762707 | 2 |
| #11762702 | 2 |
| #11762690 | 2 |
| C17×#390 | 2 |
| #2808 | 17 |