Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24909275 | C2 | semidirect |
| 2. #24905766 | C2 | semidirect |
| 3. #24905439 | C2 | semidirect |
| 4. #24905436 | C2 | semidirect |
| 7. #19127522 | C22 | semidirect |
| 11. #19127422 | C22 | semidirect |
| 12. C8×C83⋊C8 | C22 | semidirect |
| 63. Q16×C83 | M16 | semidirect |
| 67. D8×C83 | M16 | semidirect |
| 130. C83 | #11669 | semidirect |
| 184. Q16 | #13050574 | semidirect |
| 188. D8 | #13050574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909275 | 2 |
| #24905766 | 2 |
| #24905439 | 2 |
| #24905436 | 2 |
| C83×#2956 | 2 |
| #11669 | 83 |