Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#17986749 | C2 | semidirect |
| 2. #22599526 | C2 | semidirect |
| 3. #22587649 | C2 | semidirect |
| 4. #22587636 | C2 | semidirect |
| 5. #22586964 | C2 | semidirect |
| 6. #22586941 | C2 | semidirect |
| 16. #17986405 | C22 | semidirect |
| 17. #17986363 | C22 | semidirect |
| 22. #17985740 | C22 | semidirect |
| 194. C71 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986749 | 2 |
| #22599526 | 2 |
| #22587649 | 2 |
| #22587636 | 2 |
| #22586964 | 2 |
| #22586941 | 2 |
| C71×#3153 | 2 |
| #18994 | 71 |