Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 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. #26045839 | C2 | semidirect |
| 2. #26045820 | C2 | semidirect |
| 3. #26045817 | C2 | semidirect |
| 4. #26045780 | C2 | semidirect |
| 5. #26045720 | C2 | semidirect |
| 6. #26045710 | C2 | semidirect |
| 7. #104×C373 | C2 | semidirect |
| 63. C373 | #454 | semidirect |
| 70. #104 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045839 | 2 |
| #26045820 | 2 |
| #26045817 | 2 |
| #26045780 | 2 |
| #26045720 | 2 |
| #26045710 | 2 |
| #104×C373 | 2 |
| #454 | 373 |