Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #21425069 | C2 | semidirect |
| 4. #21425068 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C59×#1295 | C2 | semidirect |
| 13. #16837796 | C4 | semidirect |
| 44. #14273727 | C2×C4 | semidirect |
| 74. #97×C59 | C2×C4 | semidirect |
| 219. #1295 | D59 | semidirect |
| 250. C59 | #9003 | semidirect |
| 291. #97 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837796 | 2 |
| #21427267 | 2 |
| #21425069 | 2 |
| #21425068 | 2 |
| C2×#16837141 | 2 |
| #21421978 | 2 |
| C59×#1295 | 2 |
| #9003 | 59 |