Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 98 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. #22626270 | C2 | semidirect |
| 2. C8×#11924036 | C2 | semidirect |
| 3. #22624894 | C2 | semidirect |
| 4. #22624893 | C2 | semidirect |
| 9. #17989509 | C22 | semidirect |
| 11. C8×#10596833 | C22 | semidirect |
| 30. #14556614 | C8 | semidirect |
| 34. #14556610 | C8 | semidirect |
| 35. Q16×D73 | C8 | semidirect |
| 37. D8×D73 | C8 | semidirect |
| 76. Dic292 | C2×C8 | semidirect |
| 81. D584 | C2×C8 | semidirect |
| 105. Q16×C73 | C2×C8 | semidirect |
| 107. D8×C73 | C2×C8 | semidirect |
| 172. D73 | #1335 | semidirect |
| 178. C73 | C2×#1335 | semidirect |
| 249. Q16 | #11924036 | semidirect |
| 256. D8 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626270 | 2 |
| C8×#11924036 | 2 |
| #22624894 | 2 |
| #22624893 | 2 |
| #443×D73 | 2 |
| C2×#1335 | 73 |