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. #24916923 | C2 | semidirect |
| 2. #24912410 | C2 | semidirect |
| 3. #24906131 | C2 | semidirect |
| 4. #24905958 | C2 | semidirect |
| 5. #24905853 | C2 | semidirect |
| 6. #24905365 | C2 | semidirect |
| 7. C83×#3205 | C2 | semidirect |
| 53. C4⋊(C83⋊C8) | D4 | semidirect |
| 64. C4⋊Q8×C83 | D4 | semidirect |
| 69. #127×C83 | D4 | semidirect |
| 76. C4⋊C8×C83 | D4 | semidirect |
| 86. C2×D332 | D8 | semidirect |
| 241. #3205 | D83 | semidirect |
| 248. C83 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D83 | semidirect |
| 292. #127 | C22⋊D83 | semidirect |
| 312. C4⋊C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916923 | 2 |
| #24912410 | 2 |
| #24906131 | 2 |
| #24905958 | 2 |
| #24905853 | 2 |
| #24905365 | 2 |
| C83×#3205 | 2 |
| #10238 | 83 |