Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
714 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22608258 | C2 | semidirect |
| 2. #22607861 | C2 | semidirect |
| 3. #22607859 | C2 | semidirect |
| 60. C24×C73 | M16 | semidirect |
| 85. C22×C4×C73 | M16 | semidirect |
| 201. C73 | #11502 | semidirect |
| 255. C24 | #11924012 | semidirect |
| 280. C22×C4 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22608258 | 2 |
| #22607861 | 2 |
| #22607859 | 2 |
| C73×#2308 | 2 |
| #11502 | 73 |