Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 104 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. #22626148 | C2 | semidirect |
| 4. #22625745 | C2 | semidirect |
| 5. #22625007 | C2 | semidirect |
| 6. #22624997 | C2 | semidirect |
| 13. #17989504 | C4 | semidirect |
| 14. #17989503 | C4 | semidirect |
| 15. #17989500 | C4 | semidirect |
| 16. #17989499 | C4 | semidirect |
| 22. #17988710 | C4 | semidirect |
| 23. #17988709 | C4 | semidirect |
| 24. #17988708 | C4 | semidirect |
| 30. #444×C73 | C4 | semidirect |
| 98. Dic292 | C42 | semidirect |
| 103. D584 | C42 | semidirect |
| 125. Q16×C73 | C42 | semidirect |
| 127. D8×C73 | C42 | semidirect |
| 209. C73 | #12650 | semidirect |
| 219. #444 | #64408 | semidirect |
| 296. Q16 | C4×#64408 | semidirect |
| 303. D8 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#360 | 2 |
| #22626239 | 2 |
| #22626148 | 2 |
| #22625745 | 2 |
| #22625007 | 2 |
| #22624997 | 2 |
| #444×D73 | 2 |
| #12650 | 73 |