Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
244 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24909294 | C2 | semidirect |
| 2. D4×C83⋊C16 | C2 | semidirect |
| 4. #24905532 | C2 | semidirect |
| 5. #24905419 | C2 | semidirect |
| 6. #24905379 | C2 | semidirect |
| 7. C83×D4⋊C16 | C2 | semidirect |
| 58. C83⋊C16 | D8 | semidirect |
| 74. D4×C83 | M32 | semidirect |
| 119. D4⋊C16 | D83 | semidirect |
| 121. C83 | #12038 | semidirect |
| 190. D4 | #14581731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909294 | 2 |
| D4×C83⋊C16 | 2 |
| C8×#13050575 | 2 |
| #24905532 | 2 |
| #24905419 | 2 |
| #24905379 | 2 |
| C83×D4⋊C16 | 2 |
| #12038 | 83 |