Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 2. #26044292 | C2 | semidirect |
| 3. #26044259 | C2 | semidirect |
| 4. #26044188 | C2 | semidirect |
| 5. #26044187 | C2 | semidirect |
| 6. #26044179 | C2 | semidirect |
| 7. #137×C367 | C2 | semidirect |
| 61. C367 | #456 | semidirect |
| 65. #137 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044308 | 2 |
| #26044292 | 2 |
| #26044259 | 2 |
| #26044188 | 2 |
| #26044187 | 2 |
| #26044179 | 2 |
| #137×C367 | 2 |
| #456 | 367 |