Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
508 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 157 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×#380 | C2 |
| prime radical | C24×C17 | C23 |
| hypercenter | #380 | D17 |
| hypocenter | C17 | #2627 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11762749 | C2 | semidirect |
| 4. #11762739 | C2 | semidirect |
| 5. #11762730 | C2 | semidirect |
| 37. C22×Dic17 | Q8 | semidirect |
| 128. C17 | #2627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587610 | 2 |
| C22×#63225 | 2 |
| #11762749 | 2 |
| #11762739 | 2 |
| #11762730 | 2 |
| #11762684 | 2 |
| #11762670 | 2 |
| C17×#380 | 2 |
| #2627 | 17 |