Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 3. C2×#17989478 | C2 | semidirect |
| 4. #22625740 | C2 | semidirect |
| 5. #22625011 | C2 | semidirect |
| 6. #22624999 | C2 | semidirect |
| 10. #17989628 | C4 | semidirect |
| 11. #17989627 | C4 | semidirect |
| 18. #17989504 | C4 | semidirect |
| 19. #17989503 | C4 | semidirect |
| 25. #17988395 | C4 | semidirect |
| 26. #17988394 | C4 | semidirect |
| 27. #17988393 | C4 | semidirect |
| 28. #359×C73 | C4 | semidirect |
| 39. #14556666 | C2×C4 | semidirect |
| 44. #14556659 | C2×C4 | semidirect |
| 64. C2×#11924003 | C2×C4 | semidirect |
| 65. #14556527 | C2×C4 | semidirect |
| 68. C2×C16×C73 | C2×C4 | semidirect |
| 69. #108×C73 | C2×C4 | semidirect |
| 185. C73 | #12649 | semidirect |
| 204. #359 | #64408 | semidirect |
| 234. C2×C16 | C2×#64408 | semidirect |
| 237. #108 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626685 | 2 |
| #22626251 | 2 |
| C2×#17989478 | 2 |
| #22625740 | 2 |
| #22625011 | 2 |
| #22624999 | 2 |
| #22611657 | 2 |
| #12649 | 73 |