Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
802 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22589175 | C2 | semidirect |
| 3. #22588284 | C2 | semidirect |
| 4. #22586855 | C2 | semidirect |
| 5. #22586246 | C2 | semidirect |
| 6. #22586226 | C2 | semidirect |
| 7. C71×#2339 | C2 | semidirect |
| 8. C2×#14556153 | C4 | semidirect |
| 14. #17986000 | C4 | semidirect |
| 29. C22×D284 | C2×C4 | semidirect |
| 35. C2×#11765849 | C2×C4 | semidirect |
| 40. C2×C4⋊Dic71 | C2×C4 | semidirect |
| 160. D4×C71 | #99 | semidirect |
| 240. #2339 | 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 |
| #22589175 | 2 |
| #22588284 | 2 |
| #22586855 | 2 |
| #22586246 | 2 |
| #22586226 | 2 |
| C71×#2339 | 2 |
| #9365 | 71 |