Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24915427 | C2 | semidirect |
| 5. #24905288 | C2 | semidirect |
| 6. #24905287 | C2 | semidirect |
| 7. C83×#1272 | C2 | semidirect |
| 102. C4⋊Dic83 | SD16 | semidirect |
| 111. C2×Q8×C83 | SD16 | semidirect |
| 222. #1272 | D83 | semidirect |
| 224. C83 | #7748 | semidirect |
| 290. C2×Q8 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915427 | 2 |
| #24908698 | 2 |
| #24908553 | 2 |
| #24908550 | 2 |
| #24905288 | 2 |
| #24905287 | 2 |
| C83×#1272 | 2 |
| #7748 | 83 |