Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
686 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 14. #17988494 | C4 | semidirect |
| 17. #17988457 | C4 | semidirect |
| 20. C2×C4⋊Q8×C73 | C4 | semidirect |
| 176. C4×C73 | #328 | semidirect |
| 197. C73 | #9679 | semidirect |
| 198. C2×C4⋊Q8 | #64408 | semidirect |
| 373. C4 | #17989441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556648 | 2 |
| C2×#17989441 | 2 |
| #22625109 | 2 |
| #22618278 | 2 |
| #9679 | 73 |