Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
740 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24917256 | C2 | semidirect |
| 3. #24906131 | C2 | semidirect |
| 4. #24905962 | C2 | semidirect |
| 5. #24905853 | C2 | semidirect |
| 6. #24905365 | C2 | semidirect |
| 7. C83×#3208 | C2 | semidirect |
| 51. C4⋊(C83⋊C8) | D4 | semidirect |
| 61. C4⋊Q8×C83 | D4 | semidirect |
| 62. C4⋊Q8×C83 | D4 | semidirect |
| 74. C4⋊C8×C83 | D4 | semidirect |
| 84. C2×D332 | SD16 | semidirect |
| 222. #3208 | D83 | semidirect |
| 229. C83 | #10246 | semidirect |
| 261. C4⋊Q8 | C22⋊D83 | semidirect |
| 262. C4⋊Q8 | C22⋊D83 | semidirect |
| 291. C4⋊C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917256 | 2 |
| #24912410 | 2 |
| #24906131 | 2 |
| #24905962 | 2 |
| #24905853 | 2 |
| #24905365 | 2 |
| C83×#3208 | 2 |
| #10246 | 83 |