Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
562 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21435023 | C2 | semidirect |
| 2. C2×#16837692 | C2 | semidirect |
| 4. #21422780 | C2 | semidirect |
| 5. #21422496 | C2 | semidirect |
| 6. #21421992 | C2 | semidirect |
| 7. C59×#1460 | C2 | semidirect |
| 83. C2×D4×C59 | SD16 | semidirect |
| 208. #1460 | D59 | semidirect |
| 240. C59 | #10180 | semidirect |
| 305. C2×D4 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435023 | 2 |
| C2×#16837692 | 2 |
| #21433560 | 2 |
| #21422780 | 2 |
| #21422496 | 2 |
| #21421992 | 2 |
| C59×#1460 | 2 |
| #10180 | 59 |