Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
436 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22589280 | C2 | semidirect |
| 5. #22586786 | C2 | semidirect |
| 6. #22586189 | C2 | semidirect |
| 7. C71×#1302 | C2 | semidirect |
| 212. #1302 | D71 | semidirect |
| 214. C71 | #9051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598422 | 2 |
| #22597481 | 2 |
| #22589280 | 2 |
| #22586926 | 2 |
| #22586786 | 2 |
| #22586189 | 2 |
| C71×#1302 | 2 |
| #9051 | 71 |