Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 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. #27189805 | C2 | semidirect |
| 2. #27189804 | C2 | semidirect |
| 3. #27189787 | C2 | semidirect |
| 4. #27189782 | C2 | semidirect |
| 5. #27189781 | C2 | semidirect |
| 6. C8×#13109888 | C2 | semidirect |
| 18. #20266978 | C4 | semidirect |
| 19. #20266977 | C4 | semidirect |
| 20. #20266973 | C4 | semidirect |
| 22. SD16×C409 | C4 | semidirect |
| 51. C409 | #443 | semidirect |
| 64. SD16 | #13109888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189805 | 2 |
| #27189804 | 2 |
| #27189787 | 2 |
| #27189782 | 2 |
| #27189781 | 2 |
| C8×#13109888 | 2 |
| #27189738 | 2 |
| #443 | 409 |