Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 2. #24908290 | C2 | semidirect |
| 3. #24907614 | C2 | semidirect |
| 4. #24906141 | C2 | semidirect |
| 5. C83×#1292 | C2 | semidirect |
| 69. C4×Dic83 | D8 | semidirect |
| 141. #1292 | D83 | semidirect |
| 142. C83 | #10518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918773 | 2 |
| #24908290 | 2 |
| #24907614 | 2 |
| #24906141 | 2 |
| C83×#1292 | 2 |
| #10518 | 83 |