Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
570 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21435021 | C2 | semidirect |
| 3. #21425070 | C2 | semidirect |
| 4. #21422657 | C2 | semidirect |
| 5. #21422656 | C2 | semidirect |
| 6. #21421940 | C2 | semidirect |
| 7. C59×#3227 | C2 | semidirect |
| 127. C2×C59⋊C8 | SD16 | semidirect |
| 189. #3227 | D59 | semidirect |
| 226. C59 | #10221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435021 | 2 |
| #21434541 | 2 |
| #21425070 | 2 |
| #21422657 | 2 |
| #21422656 | 2 |
| #21421940 | 2 |
| C59×#3227 | 2 |
| #10221 | 59 |