Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #24918378 | C2 | semidirect |
| 2. #24916923 | C2 | semidirect |
| 3. #24912405 | C2 | semidirect |
| 4. #24906130 | C2 | semidirect |
| 5. #24905855 | C2 | semidirect |
| 6. #24905366 | C2 | semidirect |
| 7. C83×#1502 | C2 | semidirect |
| 58. C4⋊(C83⋊C8) | D4 | semidirect |
| 59. C4⋊(C83⋊C8) | D4 | semidirect |
| 66. C4⋊Q8×C83 | D4 | semidirect |
| 67. #127×C83 | D4 | semidirect |
| 102. C2×D332 | D8 | semidirect |
| 245. #1502 | D83 | semidirect |
| 248. C83 | #10238 | semidirect |
| 285. C4⋊Q8 | D332 | semidirect |
| 292. #127 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918378 | 2 |
| #24916923 | 2 |
| #24912405 | 2 |
| #24906130 | 2 |
| #24905855 | 2 |
| #24905366 | 2 |
| C83×#1502 | 2 |
| #10238 | 83 |