Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #21423898 | C2 | semidirect |
| 4. #21422224 | C2 | semidirect |
| 6. C2×#14273734 | C4 | semidirect |
| 10. #16837426 | C4 | semidirect |
| 12. #16837369 | C4 | semidirect |
| 15. C2×#14273638 | C4 | semidirect |
| 16. #16837201 | C4 | semidirect |
| 17. #16837199 | C4 | semidirect |
| 169. C59 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432814 | 2 |
| #21425781 | 2 |
| #21423898 | 2 |
| #21422224 | 2 |
| C59×#2126 | 2 |
| #12634 | 59 |