Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #22608525 | C2 | semidirect |
| 4. #22608353 | C2 | semidirect |
| 6. #22608220 | C2 | semidirect |
| 7. C4×#108×C73 | C2 | semidirect |
| 177. C4×#108 | D73 | semidirect |
| 183. C73 | #9728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620490 | 2 |
| #22608525 | 2 |
| #22608522 | 2 |
| #22608353 | 2 |
| #22608349 | 2 |
| #22608220 | 2 |
| C4×#108×C73 | 2 |
| #9728 | 73 |