Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24918381 | C2 | semidirect |
| 2. #24916927 | C2 | semidirect |
| 3. #24906131 | C2 | semidirect |
| 4. #24905957 | C2 | semidirect |
| 5. #24905854 | C2 | semidirect |
| 6. #24905366 | C2 | semidirect |
| 7. C83×#2541 | C2 | semidirect |
| 38. #14581792 | D4 | semidirect |
| 39. #14581789 | D4 | semidirect |
| 47. C4⋊(C83⋊C8) | D4 | semidirect |
| 48. C4⋊(C83⋊C8) | D4 | semidirect |
| 124. C2×D4×C83 | D8 | semidirect |
| 243. #2541 | D83 | semidirect |
| 248. C83 | #10238 | semidirect |
| 352. C2×D4 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918381 | 2 |
| #24916927 | 2 |
| #24906131 | 2 |
| #24905957 | 2 |
| #24905854 | 2 |
| #24905366 | 2 |
| C83×#2541 | 2 |
| #10238 | 83 |