Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
232 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #24905532 | C2 | semidirect |
| 4. #24905526 | C2 | semidirect |
| 75. C83⋊C8 | M32 | semidirect |
| 97. C83 | #12017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909266 | 2 |
| C8×#13050574 | 2 |
| #24905532 | 2 |
| #24905526 | 2 |
| C83×#2150 | 2 |
| #12017 | 83 |