Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 66. Dic68 | Q8 | semidirect |
| 141. C17 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763536 | 2 |
| #11763213 | 2 |
| #11763210 | 2 |
| #11763119 | 2 |
| #11763113 | 2 |
| #11763093 | 2 |
| C8×Dic34 | 2 |
| C4×Dic68 | 2 |
| #11762903 | 2 |
| C17×#499 | 2 |
| #3383 | 17 |