Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
578 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21435087 | C2 | semidirect |
| 2. #21435085 | C2 | semidirect |
| 3. #21434564 | C2 | semidirect |
| 4. #21422512 | C2 | semidirect |
| 5. #21422447 | C2 | semidirect |
| 6. #21421967 | C2 | semidirect |
| 7. C59×#1496 | C2 | semidirect |
| 209. #1496 | D59 | semidirect |
| 245. C59 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435087 | 2 |
| #21435085 | 2 |
| #21434564 | 2 |
| #21422512 | 2 |
| #21422447 | 2 |
| #21421967 | 2 |
| C59×#1496 | 2 |
| #10120 | 59 |