Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#17989511 | C2 | semidirect |
| 4. #22626040 | C2 | semidirect |
| 5. #22625002 | C2 | semidirect |
| 6. #22624971 | C2 | semidirect |
| 23. #17988389 | C4 | semidirect |
| 24. #17988388 | C4 | semidirect |
| 25. #17988387 | C4 | semidirect |
| 26. #357×C73 | C4 | semidirect |
| 58. C2×#11924003 | C2×C4 | semidirect |
| 59. #14556525 | C2×C4 | semidirect |
| 62. C2×C16×C73 | C2×C4 | semidirect |
| 63. #107×C73 | C2×C4 | semidirect |
| 182. C73 | #12956 | semidirect |
| 200. #357 | #64408 | semidirect |
| 226. C2×C16 | C2×#64408 | semidirect |
| 230. #107 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989628 | 2 |
| C2×#17989511 | 2 |
| C2×#17989505 | 2 |
| #22626040 | 2 |
| #22625002 | 2 |
| #22624971 | 2 |
| #22611645 | 2 |
| #12956 | 73 |