Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 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. #22582924 | C2 | semidirect |
| 2. #22582849 | C2 | semidirect |
| 3. #22582847 | C2 | semidirect |
| 4. #22582793 | C2 | semidirect |
| 5. #99×C281 | C2 | semidirect |
| 6. C23×D281 | C22 | semidirect |
| 14. C22⋊Dic281 | C22 | semidirect |
| 18. C22⋊C4×C281 | C22 | semidirect |
| 23. C22×D281 | D4 | semidirect |
| 33. C2×Dic281 | D4 | semidirect |
| 35. C23×C281 | D4 | semidirect |
| 39. C2×C4×C281 | D4 | semidirect |
| 63. C281 | B(4,𝔽2) | semidirect |
| 69. #99 | D281 | semidirect |
| 82. C22⋊C4 | C2×D281 | semidirect |
| 88. C23 | D1124 | semidirect |
| 103. C2×C4 | D1124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582924 | 2 |
| #22582849 | 2 |
| #22582847 | 2 |
| #22582793 | 2 |
| #99×C281 | 2 |
| B(4,𝔽2) | 281 |