Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 48. #14556583 | C8 | semidirect |
| 49. #14556582 | C8 | semidirect |
| 50. #14556582 | C8 | semidirect |
| 58. #125×C73 | C8 | semidirect |
| 190. C73 | #9866 | semidirect |
| 215. #125 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#10596842 | 2 |
| #22626939 | 2 |
| #125×#64408 | 2 |
| #9866 | 73 |