Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
344 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22599811 | C2 | semidirect |
| 2. #22590291 | C2 | semidirect |
| 4. #22586327 | C2 | semidirect |
| 5. #22586324 | C2 | semidirect |
| 6. #22586293 | C2 | semidirect |
| 7. C71×#2053 | C2 | semidirect |
| 175. #2053 | D71 | semidirect |
| 179. C71 | #12172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599811 | 2 |
| #22590291 | 2 |
| #22590286 | 2 |
| #22586327 | 2 |
| #22586324 | 2 |
| #22586293 | 2 |
| C71×#2053 | 2 |
| #12172 | 71 |