Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
624 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #21433167 | C2 | semidirect |
| 3. #21424062 | C2 | semidirect |
| 4. #21422224 | C2 | semidirect |
| 5. C59×#2126 | C2 | semidirect |
| 8. #16837584 | C4 | semidirect |
| 10. #16837574 | C4 | semidirect |
| 191. #2126 | D59 | semidirect |
| 219. C59 | #13053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433444 | 2 |
| #21433167 | 2 |
| #21424062 | 2 |
| #21422224 | 2 |
| C59×#2126 | 2 |
| #13053 | 59 |