Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 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. #24913111 | C2 | semidirect |
| 4. #24905356 | C2 | semidirect |
| 5. #24905329 | C2 | semidirect |
| 6. #24905320 | C2 | semidirect |
| 52. C4⋊Q8×C83 | Q8 | semidirect |
| 53. #127×C83 | Q8 | semidirect |
| 189. C83 | #10378 | semidirect |
| 212. C4⋊Q8 | Dic166 | semidirect |
| 213. #127 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24913111 | 2 |
| #24908383 | 2 |
| #24906010 | 2 |
| #24905356 | 2 |
| #24905329 | 2 |
| #24905320 | 2 |
| C83×#1505 | 2 |
| #10378 | 83 |