Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26045840 | C2 | semidirect |
| 2. #26045824 | C2 | semidirect |
| 3. #26045823 | C2 | semidirect |
| 4. #26045815 | C2 | semidirect |
| 5. #26045814 | C2 | semidirect |
| 6. Q16×D373 | C2 | semidirect |
| 7. #26045798 | C2 | semidirect |
| 8. C2×Q16×C373 | C2 | semidirect |
| 59. C373 | #578 | semidirect |
| 67. C2×Q16 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045840 | 2 |
| #26045824 | 2 |
| #26045823 | 2 |
| #26045815 | 2 |
| #26045814 | 2 |
| Q16×D373 | 2 |
| #26045798 | 2 |
| C2×Q16×C373 | 2 |
| #578 | 373 |