Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 42. Q16×C17 | Q8 | semidirect |
| 141. C17 | #3383 | semidirect |
| 145. Q16 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763535 | 2 |
| #11763213 | 2 |
| #11763211 | 2 |
| #11763210 | 2 |
| #11763116 | 2 |
| #11763114 | 2 |
| #11763092 | 2 |
| C8×Dic34 | 2 |
| Q16×Dic17 | 2 |
| C4×Q16×C17 | 2 |
| #3383 | 17 |