Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
480 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #22589482 | C2 | semidirect |
| 3. #22589481 | C2 | semidirect |
| 5. #22586165 | C2 | semidirect |
| 7. C71×#1272 | C2 | semidirect |
| 210. #1272 | D71 | semidirect |
| 212. C71 | #7755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596284 | 2 |
| #22589482 | 2 |
| #22589481 | 2 |
| #22589425 | 2 |
| #22586165 | 2 |
| #22586160 | 2 |
| C71×#1272 | 2 |
| #7755 | 71 |