Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
882 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 187 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. #21423398 | C2 | direct (N × H) |
| 3. C2×#16837144 | C2 | semidirect |
| 4. C2×C59×#564 | C2 | semidirect |
| 10. #16837144 | C22 | semidirect |
| 12. C59×#564 | C22 | semidirect |
| 67. C2×#564 | D59 | semidirect |
| 71. C2×C59 | #1658 | semidirect |
| 75. #564 | C2×D59 | semidirect |
| 84. C59 | C2×#1658 | semidirect |
| 137. C2 | #21423398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837768 | 2 |
| #21423398 | 2 |
| C2×#16837144 | 2 |
| C2×C59×#564 | 2 |
| C2×#1658 | 59 |