Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22598863 | C2 | semidirect |
| 4. #22586456 | C2 | semidirect |
| 5. #22586455 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 49. C2×Q16×C71 | Q8 | semidirect |
| 51. C2×D8×C71 | Q8 | semidirect |
| 156. C71 | #13373 | semidirect |
| 177. C2×Q16 | Dic142 | semidirect |
| 179. C2×D8 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598863 | 2 |
| #22590076 | 2 |
| #22589234 | 2 |
| #22586456 | 2 |
| #22586455 | 2 |
| #22586419 | 2 |
| C71×#2145 | 2 |
| #13373 | 71 |