Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 118 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. #22626138 | C2 | semidirect |
| 3. C4×#14556659 | C2 | semidirect |
| 4. #22625002 | C2 | semidirect |
| 9. #17989504 | C4 | semidirect |
| 15. Q16×Dic73 | C4 | semidirect |
| 18. C4×D584 | C4 | semidirect |
| 19. #17988669 | C4 | semidirect |
| 23. C4×Q16×C73 | C4 | semidirect |
| 27. #14556666 | C2×C4 | semidirect |
| 30. #14556659 | C2×C4 | semidirect |
| 78. D584 | C42 | semidirect |
| 96. Q16×C73 | C42 | semidirect |
| 150. Dic73 | #360 | semidirect |
| 163. C73 | C4×#360 | semidirect |
| 168. C4×Q16 | #64408 | semidirect |
| 232. Q16 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989504 | 2 |
| #22626138 | 2 |
| C4×#14556659 | 2 |
| #22625002 | 2 |
| C4×#14556614 | 2 |
| C4×#360 | 73 |