Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626585 | C2 | semidirect |
| 2. #22626253 | C2 | semidirect |
| 3. C2×#17989504 | C2 | semidirect |
| 4. #22626174 | C2 | semidirect |
| 5. #22625011 | C2 | semidirect |
| 6. #22624997 | C2 | semidirect |
| 25. #17988859 | C4 | semidirect |
| 26. #17988858 | C4 | semidirect |
| 27. #17988857 | C4 | semidirect |
| 32. #473×C73 | C4 | semidirect |
| 67. C2×D584 | C2×C4 | semidirect |
| 78. #14556527 | C2×C4 | semidirect |
| 84. C2×Q16×C73 | C2×C4 | semidirect |
| 86. #108×C73 | C2×C4 | semidirect |
| 236. C73 | #13005 | semidirect |
| 244. #473 | #64408 | semidirect |
| 276. C2×Q16 | C2×#64408 | semidirect |
| 305. #108 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626585 | 2 |
| #22626253 | 2 |
| C2×#17989504 | 2 |
| #22626174 | 2 |
| #22625011 | 2 |
| #22624997 | 2 |
| #22619653 | 2 |
| #13005 | 73 |