Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
448 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×#17989484 | C2 | semidirect |
| 2. C2×#17989455 | C2 | semidirect |
| 3. #22624903 | C2 | semidirect |
| 4. #22624901 | C2 | semidirect |
| 14. #17988842 | C4 | semidirect |
| 16. #17988837 | C4 | semidirect |
| 20. #17988625 | C4 | semidirect |
| 22. C2×#135×C73 | C4 | semidirect |
| 51. #14556523 | C2×C4 | semidirect |
| 52. #14556523 | C2×C4 | semidirect |
| 60. C2×Q16×C73 | C2×C4 | semidirect |
| 62. C2×D8×C73 | C2×C4 | semidirect |
| 198. C73 | #11685 | semidirect |
| 199. C2×#135 | #64408 | semidirect |
| 220. C2×Q16 | C2×#64408 | semidirect |
| 222. C2×D8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989484 | 2 |
| C2×#17989455 | 2 |
| #22624903 | 2 |
| #22624901 | 2 |
| #22619536 | 2 |
| #11685 | 73 |