Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 53. #63231 | Q8 | semidirect |
| 150. C17 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763538 | 2 |
| #11763534 | 2 |
| #11763212 | 2 |
| #11763209 | 2 |
| #11763119 | 2 |
| #11763114 | 2 |
| #11763095 | 2 |
| #11762933 | 2 |
| C4×#63231 | 2 |
| #11762901 | 2 |
| C17×#475 | 2 |
| #3383 | 17 |