Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24920599 | C2 | semidirect |
| 2. #24917184 | C2 | semidirect |
| 3. #24917126 | C2 | semidirect |
| 4. C2×#19127510 | C2 | semidirect |
| 5. #24909190 | C2 | semidirect |
| 6. #24909090 | C2 | semidirect |
| 7. C83×#1383 | C2 | semidirect |
| 50. C2×Dic332 | D4 | semidirect |
| 54. C2×D664 | D4 | semidirect |
| 83. C2×C16×C83 | D4 | semidirect |
| 85. #108×C83 | D4 | semidirect |
| 233. #1383 | D83 | semidirect |
| 234. C83 | #13318 | semidirect |
| 306. C2×C16 | D332 | semidirect |
| 308. #108 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920599 | 2 |
| #24917184 | 2 |
| #24917126 | 2 |
| C2×#19127510 | 2 |
| #24909190 | 2 |
| #24909090 | 2 |
| C83×#1383 | 2 |
| #13318 | 83 |