Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
646 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 646 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. C2×#19127896 | C2 | semidirect |
| 3. #24906132 | C2 | semidirect |
| 4. #24905862 | C2 | semidirect |
| 5. #24905784 | C2 | semidirect |
| 6. #24905358 | C2 | semidirect |
| 7. C83×#3036 | C2 | semidirect |
| 114. C2×D4×C83 | D8 | semidirect |
| 233. #3036 | D83 | semidirect |
| 239. C83 | #10176 | semidirect |
| 339. C2×D4 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918378 | 2 |
| C2×#19127896 | 2 |
| #24906132 | 2 |
| #24905862 | 2 |
| #24905784 | 2 |
| #24905358 | 2 |
| C83×#3036 | 2 |
| #10176 | 83 |