Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24918470 | C2 | semidirect |
| 3. #24905936 | C2 | semidirect |
| 4. #24905881 | C2 | semidirect |
| 5. #24905815 | C2 | semidirect |
| 6. #24905335 | C2 | semidirect |
| 7. C83×#3140 | C2 | semidirect |
| 198. #3140 | D83 | semidirect |
| 203. C83 | #10124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918470 | 2 |
| #24918450 | 2 |
| #24905936 | 2 |
| #24905881 | 2 |
| #24905815 | 2 |
| #24905335 | 2 |
| C83×#3140 | 2 |
| #10124 | 83 |