Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 560 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 |
|---|---|---|
| 1. #21433124 | C2 | semidirect |
| 3. C4×#14273643 | C2 | semidirect |
| 4. #21422694 | C2 | semidirect |
| 5. #21421962 | C2 | semidirect |
| 6. #21421961 | C2 | semidirect |
| 7. C59×#1527 | C2 | semidirect |
| 56. #14273638 | D4 | semidirect |
| 77. #97×C59 | D4 | semidirect |
| 235. #1527 | D59 | semidirect |
| 269. C59 | #9187 | semidirect |
| 309. #97 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433124 | 2 |
| #21429949 | 2 |
| C4×#14273643 | 2 |
| #21422694 | 2 |
| #21421962 | 2 |
| #21421961 | 2 |
| C59×#1527 | 2 |
| #9187 | 59 |