Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
390 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#20259238 | C2 | semidirect |
| 3. #27132627 | C2 | semidirect |
| 4. #27132431 | C2 | semidirect |
| 5. C22×M16×C191 | C2 | semidirect |
| 50. M16×C191 | D4 | semidirect |
| 93. C22×C191 | #100 | semidirect |
| 113. C191 | #1900 | semidirect |
| 115. C22×M16 | D191 | semidirect |
| 159. M16 | C22⋊D191 | semidirect |
| 211. C22 | #20259238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259296 | 2 |
| C2×#20259238 | 2 |
| #27132627 | 2 |
| #27132431 | 2 |
| C22×M16×C191 | 2 |
| #1900 | 191 |