Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22598994 | C2 | semidirect |
| 3. #22590559 | C2 | semidirect |
| 4. #22590515 | C2 | semidirect |
| 5. #22590420 | C2 | semidirect |
| 8. #22590234 | C2 | semidirect |
| 9. #22590230 | C2 | semidirect |
| 10. #22590153 | C2 | semidirect |
| 11. C71×#2239 | C2 | semidirect |
| 17. #17986399 | C22 | semidirect |
| 18. #17986377 | C22 | semidirect |
| 26. #17986106 | C22 | semidirect |
| 27. #17986105 | C22 | semidirect |
| 31. #17985823 | C22 | semidirect |
| 32. #17985819 | C22 | semidirect |
| 33. #17985814 | C22 | semidirect |
| 37. #17985776 | C22 | semidirect |
| 40. #365×C71 | C22 | semidirect |
| 41. #362×C71 | C22 | semidirect |
| 201. #2239 | D71 | semidirect |
| 209. C71 | #33693 | semidirect |
| 232. #365 | C2×D71 | semidirect |
| 235. #362 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598994 | 2 |
| #22597242 | 2 |
| #22590559 | 2 |
| #22590515 | 2 |
| #22590420 | 2 |
| #22590293 | 2 |
| #22590290 | 2 |
| #22590234 | 2 |
| #22590230 | 2 |
| #22590153 | 2 |
| C71×#2239 | 2 |
| #33693 | 71 |