Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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×Dic34 | C2 | semidirect |
| 3. #11763218 | C2 | semidirect |
| 4. #11763214 | C2 | semidirect |
| 5. #11763117 | C2 | semidirect |
| 6. #11763105 | C2 | semidirect |
| 11. C17×#446 | C2 | semidirect |
| 71. #63219 | Q8 | semidirect |
| 120. #446 | D17 | semidirect |
| 156. C17 | #3385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic34 | 2 |
| #11763519 | 2 |
| #11763218 | 2 |
| #11763214 | 2 |
| #11763117 | 2 |
| #11763105 | 2 |
| #11763100 | 2 |
| #11763090 | 2 |
| #11762911 | 2 |
| C4×#63219 | 2 |
| C17×#446 | 2 |
| #3385 | 17 |