Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
438 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22590106 | C2 | semidirect |
| 2. #22589968 | C2 | semidirect |
| 3. #22589951 | C2 | semidirect |
| 4. #22589945 | C2 | semidirect |
| 26. C2×C71⋊C16 | D4 | semidirect |
| 145. C71 | #13200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590106 | 2 |
| #22589968 | 2 |
| #22589951 | 2 |
| #22589945 | 2 |
| C71×#2929 | 2 |
| #13200 | 71 |