Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
316 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22590613 | C2 | semidirect |
| 3. #22587734 | C2 | semidirect |
| 4. #22586395 | C2 | semidirect |
| 5. Q8⋊(C71⋊C16) | C2 | semidirect |
| 68. D8×C71 | Q16 | semidirect |
| 134. C71 | #12404 | semidirect |
| 190. D8 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590613 | 2 |
| #22590477 | 2 |
| #22587734 | 2 |
| #22586395 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586301 | 2 |
| Q8×D8×C71 | 2 |
| #12404 | 71 |