Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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×C8×D379 | C2 | semidirect |
| 3. #27131289 | C2 | semidirect |
| 4. #27131255 | C2 | semidirect |
| 5. #27131253 | C2 | semidirect |
| 6. #27131251 | C2 | semidirect |
| 7. #103×C379 | C2 | semidirect |
| 9. #20258607 | C4 | semidirect |
| 57. C379 | #416 | semidirect |
| 63. #103 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258607 | 2 |
| C2×C8×D379 | 2 |
| #27131289 | 2 |
| #27131255 | 2 |
| #27131253 | 2 |
| #27131251 | 2 |
| #103×C379 | 2 |
| #416 | 379 |