Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22591450 | C2 | semidirect |
| 3. #22586963 | C2 | semidirect |
| 4. #22586848 | C2 | semidirect |
| 5. #22586233 | C2 | semidirect |
| 6. #22586232 | C2 | semidirect |
| 7. C71×#1505 | C2 | semidirect |
| 11. #17986391 | C4 | semidirect |
| 12. #17986386 | C4 | semidirect |
| 58. #14556039 | C2×C4 | semidirect |
| 66. C4⋊Q8×C71 | C2×C4 | semidirect |
| 67. #127×C71 | C2×C4 | semidirect |
| 231. #1505 | D71 | semidirect |
| 234. C71 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D71 | semidirect |
| 272. #127 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598808 | 2 |
| #22591450 | 2 |
| #22586963 | 2 |
| #22586848 | 2 |
| #22586233 | 2 |
| #22586232 | 2 |
| C71×#1505 | 2 |
| #9441 | 71 |