Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
334 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24907583 | C2 | semidirect |
| 3. #24906238 | C2 | semidirect |
| 4. #24906234 | C2 | semidirect |
| 7. C83×#1274 | C2 | semidirect |
| 135. #1274 | D83 | semidirect |
| 136. C83 | #10665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908295 | 2 |
| #24907583 | 2 |
| #24906238 | 2 |
| #24906234 | 2 |
| #24905863 | 2 |
| C83×#1274 | 2 |
| #10665 | 83 |