Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
426 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22626295 | C2 | semidirect |
| 2. #22625486 | C2 | semidirect |
| 3. #22624890 | C2 | semidirect |
| 4. #22624889 | C2 | semidirect |
| 9. #17989476 | C22 | semidirect |
| 11. #17989448 | C22 | semidirect |
| 73. D584 | M16 | semidirect |
| 91. D8×C73 | M16 | semidirect |
| 163. C73 | #11663 | semidirect |
| 233. D8 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626295 | 2 |
| #22625486 | 2 |
| #22624890 | 2 |
| #22624889 | 2 |
| C4×D8×D73 | 2 |
| #11663 | 73 |