Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1214 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 187 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. #24917394 | C2 | semidirect |
| 3. #24908680 | C2 | semidirect |
| 4. #24907911 | C2 | semidirect |
| 5. #24907677 | C2 | semidirect |
| 6. #24907421 | C2 | semidirect |
| 7. #24907387 | C2 | semidirect |
| 8. C83×#2310 | C2 | semidirect |
| 207. #2310 | D83 | semidirect |
| 213. C83 | #24023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921114 | 2 |
| #24917394 | 2 |
| #24908680 | 2 |
| #24907911 | 2 |
| #24907677 | 2 |
| #24907421 | 2 |
| #24907387 | 2 |
| C83×#2310 | 2 |
| #24023 | 83 |