Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22599682 | C2 | semidirect |
| 4. #22589283 | C2 | semidirect |
| 6. #22586189 | C2 | semidirect |
| 7. C71×#1503 | C2 | semidirect |
| 201. #1503 | D71 | semidirect |
| 203. C71 | #10195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599682 | 2 |
| #22599283 | 2 |
| #22598716 | 2 |
| #22589283 | 2 |
| #22589267 | 2 |
| #22586189 | 2 |
| C71×#1503 | 2 |
| #10195 | 71 |