Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22590615 | C2 | semidirect |
| 4. #22587734 | C2 | semidirect |
| 5. #22586394 | C2 | semidirect |
| 7. C71×Q8⋊C16 | C2 | semidirect |
| 62. D568 | Q16 | semidirect |
| 132. Q8⋊C16 | D71 | semidirect |
| 134. C71 | #12404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D568 | 2 |
| #22590615 | 2 |
| #22590478 | 2 |
| #22587734 | 2 |
| #22586394 | 2 |
| #22586302 | 2 |
| C71×Q8⋊C16 | 2 |
| #12404 | 71 |