Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
164 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 75 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. #24905660 | C2 | semidirect |
| 4. #24905599 | C2 | semidirect |
| 5. C83×#1398 | C2 | semidirect |
| 74. #1398 | D83 | semidirect |
| 75. C83 | #13643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909061 | 2 |
| #24905660 | 2 |
| #24905602 | 2 |
| #24905599 | 2 |
| C83×#1398 | 2 |
| #13643 | 83 |