Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
642 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21435474 | C2 | semidirect |
| 2. #21435014 | C2 | semidirect |
| 3. #21424937 | C2 | semidirect |
| 4. #21422687 | C2 | semidirect |
| 5. #21422513 | C2 | semidirect |
| 6. #21421986 | C2 | semidirect |
| 7. C59×#3151 | C2 | semidirect |
| 199. #3151 | D59 | semidirect |
| 234. C59 | #10104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435474 | 2 |
| #21435014 | 2 |
| #21424937 | 2 |
| #21422687 | 2 |
| #21422513 | 2 |
| #21421986 | 2 |
| C59×#3151 | 2 |
| #10104 | 59 |