Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22612154 | C2 | semidirect |
| 2. #22612068 | C2 | semidirect |
| 3. #22609320 | C2 | semidirect |
| 4. #22607977 | C2 | semidirect |
| 5. #22607892 | C2 | semidirect |
| 6. D4⋊#11924003 | C2 | semidirect |
| 8. #17988992 | C22 | semidirect |
| 11. C4⋊#11924003 | C22 | semidirect |
| 14. C4×#11924003 | C22 | semidirect |
| 15. #17988340 | C22 | semidirect |
| 80. D8×C73 | SD16 | semidirect |
| 159. C73 | #12368 | semidirect |
| 227. D8 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612154 | 2 |
| #22612068 | 2 |
| #22609320 | 2 |
| #22607977 | 2 |
| #22607892 | 2 |
| D4⋊#11924003 | 2 |
| D4×D8×C73 | 2 |
| #12368 | 73 |