Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 4. #22610667 | C2 | semidirect |
| 5. #22608041 | C2 | semidirect |
| 6. #22608010 | C2 | semidirect |
| 7. C2×#365×C73 | C2 | semidirect |
| 18. #17988392 | C4 | semidirect |
| 19. #17988389 | C4 | semidirect |
| 71. Dic292 | C4⋊C4 | semidirect |
| 75. D584 | C4⋊C4 | semidirect |
| 157. C2×#365 | D73 | semidirect |
| 163. C73 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988708 | 2 |
| C2×#17988396 | 2 |
| #22611644 | 2 |
| #22610667 | 2 |
| #22608041 | 2 |
| #22608010 | 2 |
| C2×#365×C73 | 2 |
| #12955 | 73 |