Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 204 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×#3624 | C2 | semidirect |
| 2. #11763837 | C2 | semidirect |
| 3. #11763827 | C2 | semidirect |
| 4. #11763810 | C2 | semidirect |
| 20. #63256 | C8 | semidirect |
| 36. Q8×C17 | C2×C8 | semidirect |
| 43. D68 | C2×C8 | semidirect |
| 47. C4×D17 | C2×C8 | semidirect |
| 84. C17 | #2988 | semidirect |
| 102. Q8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3624 | 2 |
| #11763837 | 2 |
| #11763827 | 2 |
| #11763810 | 2 |
| C4×#63256 | 2 |
| #2988 | 17 |