Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
446 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 106 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. #22626264 | C2 | semidirect |
| 3. #22625866 | C2 | semidirect |
| 4. #22625002 | C2 | semidirect |
| 15. Q16×Dic73 | C4 | semidirect |
| 18. C4×D584 | C4 | semidirect |
| 19. #17988669 | C4 | semidirect |
| 23. C4×Q16×C73 | C4 | semidirect |
| 85. D584 | C4⋊C4 | semidirect |
| 106. Q16×C73 | C4⋊C4 | semidirect |
| 161. C4×C73 | #360 | semidirect |
| 166. Dic73 | #360 | semidirect |
| 181. C73 | #12816 | semidirect |
| 186. C4×Q16 | #64408 | semidirect |
| 255. Q16 | C4⋊#64408 | semidirect |
| 342. C4 | #17989504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626264 | 2 |
| C2×#17989504 | 2 |
| #22625866 | 2 |
| #22625002 | 2 |
| C4×#14556614 | 2 |
| #12816 | 73 |