Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. #11763122 | C2 | semidirect |
| 3. #11763104 | C2 | semidirect |
| 4. #11763009 | C2 | semidirect |
| 5. #11762948 | C2 | semidirect |
| 6. #11762907 | C2 | semidirect |
| 7. #11762866 | C2 | semidirect |
| 8. C2×C4×Q8×C17 | C2 | semidirect |
| 68. Q8×C17 | #41 | semidirect |
| 108. C2×C4×Q8 | D17 | semidirect |
| 144. C17 | #3112 | semidirect |
| 181. Q8 | #63252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11763122 | 2 |
| #11763104 | 2 |
| #11763009 | 2 |
| #11762948 | 2 |
| #11762907 | 2 |
| #11762866 | 2 |
| C2×C4×Q8×C17 | 2 |
| #3112 | 17 |