Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
578 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 79 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. #24918454 | C2 | semidirect |
| 2. #24918452 | C2 | semidirect |
| 3. #24917931 | C2 | semidirect |
| 4. #24905879 | C2 | semidirect |
| 5. #24905814 | C2 | semidirect |
| 6. #24905334 | C2 | semidirect |
| 7. C83×#1496 | C2 | semidirect |
| 216. #1496 | D83 | semidirect |
| 220. C83 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918454 | 2 |
| #24918452 | 2 |
| #24917931 | 2 |
| #24905879 | 2 |
| #24905814 | 2 |
| #24905334 | 2 |
| C83×#1496 | 2 |
| #10120 | 83 |