Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21435306 | C2 | semidirect |
| 3. #21425078 | C2 | semidirect |
| 4. #21422609 | C2 | semidirect |
| 6. #21422006 | C2 | semidirect |
| 224. C59 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435483 | 2 |
| #21435306 | 2 |
| #21425078 | 2 |
| #21422609 | 2 |
| #21422604 | 2 |
| #21422006 | 2 |
| C59×#3216 | 2 |
| #10215 | 59 |