Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #21432756 | C2 | semidirect |
| 3. #21424193 | C2 | semidirect |
| 6. #21421943 | C2 | semidirect |
| 7. C59×#1293 | C2 | semidirect |
| 17. C2×#14273661 | C4 | semidirect |
| 18. C2×#14273659 | C4 | semidirect |
| 20. C2×#14273649 | C4 | semidirect |
| 21. C2×#14273649 | C4 | semidirect |
| 221. #1293 | D59 | semidirect |
| 256. C59 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837727 | 2 |
| #21432756 | 2 |
| #21424193 | 2 |
| #21422613 | 2 |
| #21422457 | 2 |
| #21421943 | 2 |
| C59×#1293 | 2 |
| #9242 | 59 |