Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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×#389 | C2 |
| hypercenter | #389 | D17 |
| hypocenter | C17 | #2682 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587580 | C2 | semidirect |
| 2. C2×#10587581 | C2 | semidirect |
| 3. #11762731 | C2 | semidirect |
| 4. #11762726 | C2 | semidirect |
| 5. #11762719 | C2 | semidirect |
| 6. #11762711 | C2 | semidirect |
| 7. #11762711 | C2 | semidirect |
| 8. #11762683 | C2 | semidirect |
| 9. C17×#389 | C2 | semidirect |
| 53. C2×D68 | D4 | semidirect |
| 59. C4⋊C4×C17 | D4 | semidirect |
| 148. #389 | D17 | semidirect |
| 182. C17 | #2682 | semidirect |
| 212. C4⋊C4 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587580 | 2 |
| C2×#10587581 | 2 |
| #11762731 | 2 |
| #11762726 | 2 |
| #11762719 | 2 |
| #11762711 | 2 |
| #11762683 | 2 |
| C17×#389 | 2 |
| #2682 | 17 |