Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 4. C2×C4⋊#10596833 | C4 | semidirect |
| 8. C2×#14556646 | C4 | semidirect |
| 10. #17989465 | C4 | semidirect |
| 14. #17988354 | C4 | semidirect |
| 15. #342×C73 | C4 | semidirect |
| 167. C73 | #7283 | semidirect |
| 179. #342 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626056 | 2 |
| #22625678 | 2 |
| #22609718 | 2 |
| #7283 | 73 |