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. #22626146 | C2 | semidirect |
| 4. #22625739 | C2 | semidirect |
| 5. #22625012 | C2 | semidirect |
| 6. #22624998 | C2 | semidirect |
| 10. #17989628 | C4 | semidirect |
| 11. #17989628 | C4 | semidirect |
| 12. #17989627 | C4 | semidirect |
| 13. #17989627 | C4 | semidirect |
| 21. #17989502 | C4 | semidirect |
| 22. #17989501 | C4 | semidirect |
| 29. #17988398 | C4 | semidirect |
| 30. #17988397 | C4 | semidirect |
| 31. #17988396 | C4 | semidirect |
| 32. #360×C73 | C4 | semidirect |
| 47. #14556664 | C2×C4 | semidirect |
| 49. #14556662 | C2×C4 | semidirect |
| 74. #14556531 | C2×C4 | semidirect |
| 78. #14556523 | C2×C4 | semidirect |
| 80. M32×C73 | C2×C4 | semidirect |
| 81. #106×C73 | C2×C4 | semidirect |
| 212. C73 | #12649 | semidirect |
| 232. #360 | #64408 | semidirect |
| 266. M32 | C2×#64408 | semidirect |
| 276. #106 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626685 | 2 |
| #22626245 | 2 |
| #22626146 | 2 |
| #22625739 | 2 |
| #22625012 | 2 |
| #22624998 | 2 |
| #22611665 | 2 |
| #12649 | 73 |