Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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×#19154564 | C2 | semidirect |
| 3. #26044268 | C2 | semidirect |
| 4. #26044196 | C2 | semidirect |
| 5. #26044180 | C2 | semidirect |
| 6. #26044177 | C2 | semidirect |
| 7. #137×C367 | C2 | semidirect |
| 51. C367 | #471 | semidirect |
| 53. #137 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044286 | 2 |
| C2×#19154564 | 2 |
| #26044268 | 2 |
| #26044196 | 2 |
| #26044180 | 2 |
| #26044177 | 2 |
| #137×C367 | 2 |
| #471 | 367 |