Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22599542 | C2 | semidirect |
| 5. #22586943 | C2 | semidirect |
| 6. #22586233 | C2 | semidirect |
| 7. C71×#1506 | C2 | semidirect |
| 184. #1506 | D71 | semidirect |
| 186. C71 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599542 | 2 |
| #22598716 | 2 |
| #22594283 | 2 |
| #22587053 | 2 |
| #22586943 | 2 |
| #22586233 | 2 |
| C71×#1506 | 2 |
| #10097 | 71 |