Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
460 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#595 |
| commutator, socle | C22×C17 | C23×C4 |
| Fitting | C17×C4⋊Q8 | C4 |
| prime radical, cosocle | C22×D17 | C24 |
| hypercenter | C4⋊Q8 | #595 |
| hypocenter | C17 | #2331 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C17×C4⋊Q8 | C4 | semidirect |
| 15. #10587630 | C4 | semidirect |
| 18. #10587574 | C4 | semidirect |
| 19. #10587574 | C4 | semidirect |
| 21. #10587555 | C4 | semidirect |
| 43. C4×#595 | Q8 | semidirect |
| 115. C4⋊Q8 | #595 | semidirect |
| 130. C17 | #2331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#595)⋊Q8 | 2 |
| #11763760 | 2 |
| #11763758 | 2 |
| #11763753 | 2 |
| C4⋊C4×#595 | 2 |
| #11763745 | 2 |
| C4⋊Q8×D17 | 2 |
| #2331 | 17 |