Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
642 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 642 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 |
|---|---|---|
| 2. #24917922 | C2 | semidirect |
| 3. C2×#19128047 | C2 | semidirect |
| 4. #24906136 | C2 | semidirect |
| 5. #24905913 | C2 | semidirect |
| 6. #24905301 | C2 | semidirect |
| 7. C83×#1965 | C2 | semidirect |
| 115. M16×C83 | D8 | semidirect |
| 192. #1965 | D83 | semidirect |
| 196. C83 | #10168 | semidirect |
| 293. M16 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918381 | 2 |
| #24917922 | 2 |
| C2×#19128047 | 2 |
| #24906136 | 2 |
| #24905913 | 2 |
| #24905301 | 2 |
| C83×#1965 | 2 |
| #10168 | 83 |