Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
588 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 210 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 | C4×C4⋊Q8 |
| 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 |
|---|---|---|
| 18. C17×C4⋊Q8 | C4 | semidirect |
| 19. #10587630 | C4 | semidirect |
| 21. #10587574 | C4 | semidirect |
| 23. #10587555 | C4 | semidirect |
| 44. C4×#595 | Q8 | semidirect |
| 85. #595 | C4⋊Q8 | direct (N × H) |
| 88. C4×C17 | C4×Q8 | semidirect |
| 91. Dic17 | C4×Q8 | semidirect |
| 108. C4⋊Q8 | #595 | direct (N × H) |
| 121. C17 | C4×C4⋊Q8 | semidirect |
| 187. C4 | Q8×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#595 | 2 |
| (C2×#595)⋊Q8 | 2 |
| #11763760 | 2 |
| #11763755 | 2 |
| C4⋊C4×#595 | 2 |
| C42×#595 | 2 |
| C4⋊Q8×D17 | 2 |
| C4×C4⋊Q8 | 17 |