Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
414 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #24906057 | C2 | semidirect |
| 4. #24905885 | C2 | semidirect |
| 6. #24905752 | C2 | semidirect |
| 7. C4×#108×C83 | C2 | semidirect |
| 177. C4×#108 | D83 | semidirect |
| 183. C83 | #9728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918022 | 2 |
| #24906057 | 2 |
| #24906054 | 2 |
| #24905885 | 2 |
| #24905881 | 2 |
| #24905752 | 2 |
| C4×#108×C83 | 2 |
| #9728 | 83 |