Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1146 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1146 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 |
|---|---|---|
| 2. C2×#17985795 | C2 | semidirect |
| 3. #22588264 | C2 | semidirect |
| 4. C71×#1784 | C2 | semidirect |
| 15. C2×#14556047 | C22 | semidirect |
| 20. C2×#101×C71 | C22 | semidirect |
| 172. C22×C71 | #355 | semidirect |
| 198. #1784 | D71 | semidirect |
| 199. C71 | #12699 | semidirect |
| 213. C2×#101 | C2×D71 | semidirect |
| 372. C22 | #17985795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556117 | 2 |
| C2×#17985795 | 2 |
| #22588264 | 2 |
| C71×#1784 | 2 |
| #12699 | 71 |