Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#3633 | C2 | semidirect |
| 15. C2×Q8×C17 | C8 | semidirect |
| 16. Q8×D17 | C8 | semidirect |
| 19. C2×Dic34 | C8 | semidirect |
| 63. C17 | #2982 | semidirect |
| 67. C2×Q8 | #3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3633 | 2 |
| #11763922 | 2 |
| C2×Q8×#595 | 2 |
| #2982 | 17 |