Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
332 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4×C16×D59 | C2 | semidirect |
| 3. #21422858 | C2 | semidirect |
| 4. #21422061 | C2 | semidirect |
| 5. #21422059 | C2 | semidirect |
| 6. #21422057 | C2 | semidirect |
| 7. C59×#1331 | C2 | semidirect |
| 155. #1331 | D59 | semidirect |
| 180. C59 | #11673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434664 | 2 |
| C4×C16×D59 | 2 |
| #21422858 | 2 |
| #21422061 | 2 |
| #21422059 | 2 |
| #21422057 | 2 |
| C59×#1331 | 2 |
| #11673 | 59 |