Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24915416 | C2 | semidirect |
| 5. #24905288 | C2 | semidirect |
| 6. #24905287 | C2 | semidirect |
| 7. C83×#1271 | C2 | semidirect |
| 118. C4⋊C4×C83 | SD16 | semidirect |
| 216. #1271 | D83 | semidirect |
| 217. C83 | #7747 | semidirect |
| 327. C4⋊C4 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915416 | 2 |
| #24908698 | 2 |
| #24908697 | 2 |
| #24908553 | 2 |
| #24905288 | 2 |
| #24905287 | 2 |
| C83×#1271 | 2 |
| #7747 | 83 |