Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
572 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×#14556659 | C2 | semidirect |
| 2. C2×#17989503 | C2 | semidirect |
| 3. #22626159 | C2 | semidirect |
| 4. #22625002 | C2 | semidirect |
| 17. #17988829 | C4 | semidirect |
| 18. #17988828 | C4 | semidirect |
| 19. #17988820 | C4 | semidirect |
| 24. #466×C73 | C4 | semidirect |
| 35. #14556659 | D4 | semidirect |
| 40. C2×Dic292 | C2×C4 | semidirect |
| 57. #14556525 | C2×C4 | semidirect |
| 62. C2×D8×C73 | C2×C4 | semidirect |
| 65. #107×C73 | C2×C4 | semidirect |
| 173. C22×C73 | #360 | semidirect |
| 181. C2×D73 | #360 | semidirect |
| 208. C73 | #13001 | semidirect |
| 217. #466 | #64408 | semidirect |
| 235. C2×D8 | C2×#64408 | semidirect |
| 261. #107 | C2×#64408 | semidirect |
| 385. C22 | #17989503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556659 | 2 |
| C2×#17989503 | 2 |
| #22626159 | 2 |
| #22625002 | 2 |
| #22619510 | 2 |
| #13001 | 73 |