Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#17985814 | C2 | semidirect |
| 5. #22590059 | C2 | semidirect |
| 6. #22589945 | C2 | semidirect |
| 7. C71×#1833 | C2 | semidirect |
| 15. #17986383 | C4 | semidirect |
| 16. #17986379 | C4 | semidirect |
| 175. #1833 | D71 | semidirect |
| 176. C71 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598834 | 2 |
| C2×#17985814 | 2 |
| #22590075 | 2 |
| #22590067 | 2 |
| #22590059 | 2 |
| #22589945 | 2 |
| C71×#1833 | 2 |
| #13216 | 71 |