Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 92 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. #22626283 | C2 | semidirect |
| 4. #22625003 | C2 | semidirect |
| 19. #17988369 | C4 | semidirect |
| 20. #17988368 | C4 | semidirect |
| 21. #349×C73 | C4 | semidirect |
| 50. #14556531 | C2×C4 | semidirect |
| 54. M32×C73 | C2×C4 | semidirect |
| 171. C73 | #12923 | semidirect |
| 186. #349 | #64408 | semidirect |
| 210. M32 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626584 | 2 |
| #22626283 | 2 |
| #22625809 | 2 |
| #22625003 | 2 |
| #349×D73 | 2 |
| #12923 | 73 |