Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
458 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22621606 | C2 | semidirect |
| 2. #22612180 | C2 | semidirect |
| 3. #22611967 | C2 | semidirect |
| 4. #22609287 | C2 | semidirect |
| 5. #22607891 | C2 | semidirect |
| 6. #22607885 | C2 | semidirect |
| 7. C73×#1361 | C2 | semidirect |
| 12. #17988964 | C22 | semidirect |
| 20. C4×#11924003 | C22 | semidirect |
| 23. C4⋊C16×C73 | C22 | semidirect |
| 24. #335×C73 | C22 | semidirect |
| 75. D584 | D8 | semidirect |
| 124. D292 | D16 | semidirect |
| 167. #1361 | D73 | semidirect |
| 170. C73 | #12316 | semidirect |
| 183. C4⋊C16 | C2×D73 | semidirect |
| 186. #335 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621606 | 2 |
| #22612180 | 2 |
| #22611967 | 2 |
| #22609287 | 2 |
| #22607891 | 2 |
| #22607885 | 2 |
| C73×#1361 | 2 |
| #12316 | 73 |