Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909719 | C2 | semidirect |
| 2. #24906828 | C2 | semidirect |
| 4. #24905535 | C2 | semidirect |
| 5. #24905513 | C2 | semidirect |
| 6. #24905510 | C2 | semidirect |
| 7. C83×#2169 | C2 | semidirect |
| 73. C16×C83 | D8 | semidirect |
| 119. #2169 | D83 | semidirect |
| 125. C83 | #12435 | semidirect |
| 191. C16 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909719 | 2 |
| #24906828 | 2 |
| #24906818 | 2 |
| #24905535 | 2 |
| #24905513 | 2 |
| #24905510 | 2 |
| C83×#2169 | 2 |
| #12435 | 83 |