Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 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. #24918378 | C2 | semidirect |
| 2. #24908287 | C2 | semidirect |
| 3. #24906023 | C2 | semidirect |
| 4. #24905308 | C2 | semidirect |
| 5. C83×#3150 | C2 | semidirect |
| 76. C2×C8×C83 | D8 | semidirect |
| 138. #3150 | D83 | semidirect |
| 142. C83 | #10218 | semidirect |
| 212. C2×C8 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918378 | 2 |
| #24908287 | 2 |
| #24906023 | 2 |
| #24905308 | 2 |
| C83×#3150 | 2 |
| #10218 | 83 |