Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 173 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×#391 | C2 |
| prime radical | C2×#10587581 | C2 |
| hypercenter | #391 | D17 |
| hypocenter | C17 | #2436 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D17 | C2 | semidirect |
| 2. C2×#10587633 | C2 | semidirect |
| 3. C2×#10587561 | C2 | semidirect |
| 5. #11762722 | C2 | semidirect |
| 6. #11762714 | C2 | semidirect |
| 7. #11762687 | C2 | semidirect |
| 8. C4×#63227 | C2 | semidirect |
| 9. C17×#391 | C2 | semidirect |
| 37. C2×Q8×C17 | D4 | semidirect |
| 62. C2×Dic34 | D4 | semidirect |
| 123. C2×D17 | #124 | semidirect |
| 137. #391 | D17 | semidirect |
| 170. C17 | #2436 | semidirect |
| 182. C2×Q8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D17 | 2 |
| C2×#10587633 | 2 |
| C2×#10587561 | 2 |
| C2×#10587581 | 2 |
| #11762722 | 2 |
| #11762714 | 2 |
| #11762687 | 2 |
| C4×#63227 | 2 |
| C17×#391 | 2 |
| #2436 | 17 |