Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
332 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 3. #22625079 | C2 | semidirect |
| 4. #22625078 | C2 | semidirect |
| 5. #22625060 | C2 | semidirect |
| 6. #22625060 | C2 | semidirect |
| 16. #17989198 | C4 | semidirect |
| 19. #17988951 | C4 | semidirect |
| 25. #17988646 | C4 | semidirect |
| 26. #492×C73 | C4 | semidirect |
| 41. #14556583 | C2×C4 | semidirect |
| 56. #14556502 | C2×C4 | semidirect |
| 59. C4⋊Q8×C73 | C2×C4 | semidirect |
| 61. C4×C8×C73 | C2×C4 | semidirect |
| 171. C73 | #13607 | semidirect |
| 175. #492 | #64408 | semidirect |
| 198. C4⋊Q8 | C2×#64408 | semidirect |
| 225. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626231 | 2 |
| #22626207 | 2 |
| #22625079 | 2 |
| #22625078 | 2 |
| #22625060 | 2 |
| #22620996 | 2 |
| #13607 | 73 |