Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590615 | C2 | semidirect |
| 3. #22586542 | C2 | semidirect |
| 5. C71×C4⋊C32 | C2 | semidirect |
| 19. D1136 | Q8 | semidirect |
| 74. C4⋊C32 | D71 | semidirect |
| 76. C71 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590615 | 2 |
| C4×D1136 | 2 |
| #22586542 | 2 |
| #22586519 | 2 |
| C71×C4⋊C32 | 2 |
| #13705 | 71 |