Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
802 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 802 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. #22591170 | C2 | semidirect |
| 3. #22589176 | C2 | semidirect |
| 4. #22586857 | C2 | semidirect |
| 5. #22586247 | C2 | semidirect |
| 6. #22586226 | C2 | semidirect |
| 7. C71×#1789 | C2 | semidirect |
| 8. C2×#14556153 | C4 | semidirect |
| 14. #17986000 | C4 | semidirect |
| 29. C22×D284 | C2×C4 | semidirect |
| 35. C2×#11765849 | C2×C4 | semidirect |
| 42. C2×C4⋊Dic71 | C2×C4 | semidirect |
| 160. D4×C71 | #99 | semidirect |
| 242. #1789 | D71 | semidirect |
| 246. C71 | #9365 | semidirect |
| 404. D4 | #14556042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597592 | 2 |
| #22591170 | 2 |
| #22589176 | 2 |
| #22586857 | 2 |
| #22586247 | 2 |
| #22586226 | 2 |
| C71×#1789 | 2 |
| #9365 | 71 |