Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 1. C2×#19154565 | C2 | semidirect |
| 2. C2×#19154560 | C2 | semidirect |
| 3. #26044241 | C2 | semidirect |
| 5. #26044194 | C2 | semidirect |
| 6. #26044186 | C2 | semidirect |
| 7. #102×C367 | C2 | semidirect |
| 30. C367⋊C8 | D4 | semidirect |
| 55. C367 | #468 | semidirect |
| 63. #102 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19154565 | 2 |
| C2×#19154560 | 2 |
| #26044241 | 2 |
| #26044232 | 2 |
| #26044194 | 2 |
| #26044186 | 2 |
| #102×C367 | 2 |
| #468 | 367 |