Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 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. #24918383 | C2 | semidirect |
| 2. #24916927 | C2 | semidirect |
| 3. #24912409 | C2 | semidirect |
| 4. #24906130 | C2 | semidirect |
| 5. #24905959 | C2 | semidirect |
| 6. #24905365 | C2 | semidirect |
| 7. C83×#1478 | C2 | semidirect |
| 42. #14581792 | D4 | semidirect |
| 47. #14581789 | D4 | semidirect |
| 60. C4⋊(C83⋊C8) | D4 | semidirect |
| 75. C4⋊C8×C83 | D4 | semidirect |
| 127. C2×D4×C83 | D8 | semidirect |
| 246. #1478 | D83 | semidirect |
| 248. C83 | #10238 | semidirect |
| 312. C4⋊C8 | C22⋊D83 | semidirect |
| 352. C2×D4 | D664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918383 | 2 |
| #24916927 | 2 |
| #24912409 | 2 |
| #24906130 | 2 |
| #24905959 | 2 |
| #24905365 | 2 |
| C83×#1478 | 2 |
| #10238 | 83 |