Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21422270 | C2 | semidirect |
| 4. #21422255 | C2 | semidirect |
| 6. #16838014 | C4 | semidirect |
| 8. #16837774 | C4 | semidirect |
| 9. #16837766 | C4 | semidirect |
| 15. #16837463 | C4 | semidirect |
| 28. #14273727 | C2×C4 | semidirect |
| 30. #14273719 | C2×C4 | semidirect |
| 42. #14273638 | C2×C4 | semidirect |
| 43. C4×C59⋊C8 | C2×C4 | semidirect |
| 175. C59 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435168 | 2 |
| #21425788 | 2 |
| #21422270 | 2 |
| #21422255 | 2 |
| C59×#2127 | 2 |
| #13607 | 59 |