Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#17985123 | C2 | semidirect |
| 2. C22×#14555886 | C2 | semidirect |
| 3. #22582853 | C2 | semidirect |
| 4. #22582812 | C2 | semidirect |
| 5. #22582800 | C2 | semidirect |
| 6. #22582799 | C2 | semidirect |
| 7. #121×C281 | C2 | semidirect |
| 27. #14555886 | D4 | semidirect |
| 43. C22×C281 | D8 | semidirect |
| 59. C281 | #466 | semidirect |
| 64. #121 | D281 | semidirect |
| 106. C22 | #17985123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985123 | 2 |
| C22×#14555886 | 2 |
| #22582853 | 2 |
| #22582812 | 2 |
| #22582800 | 2 |
| #22582799 | 2 |
| #121×C281 | 2 |
| #466 | 281 |