Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22596931 | C2 | semidirect |
| 3. #22590077 | C2 | semidirect |
| 4. C2×#17985808 | C2 | semidirect |
| 5. #22589969 | C2 | semidirect |
| 6. #22586454 | C2 | semidirect |
| 7. C71×#1383 | C2 | semidirect |
| 13. #17986275 | C4 | semidirect |
| 14. #17986270 | C4 | semidirect |
| 40. C2×Dic284 | C2×C4 | semidirect |
| 42. C2×D568 | C2×C4 | semidirect |
| 73. #108×C71 | C2×C4 | semidirect |
| 200. #1383 | D71 | semidirect |
| 201. C71 | #13005 | semidirect |
| 260. #108 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598061 | 2 |
| #22596931 | 2 |
| #22590077 | 2 |
| C2×#17985808 | 2 |
| #22589969 | 2 |
| #22586454 | 2 |
| C71×#1383 | 2 |
| #13005 | 71 |