Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
678 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22599461 | C2 | semidirect |
| 3. #22589168 | C2 | semidirect |
| 4. #22587012 | C2 | semidirect |
| 5. #22587008 | C2 | semidirect |
| 6. #22586173 | C2 | semidirect |
| 7. C71×#2858 | C2 | semidirect |
| 117. C42×C71 | D8 | semidirect |
| 194. #2858 | D71 | semidirect |
| 199. C71 | #10284 | semidirect |
| 309. C42 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599461 | 2 |
| #22599258 | 2 |
| #22589168 | 2 |
| #22587012 | 2 |
| #22587008 | 2 |
| #22586173 | 2 |
| C71×#2858 | 2 |
| #10284 | 71 |