Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1010 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16838152 | C2 | semidirect |
| 2. C2×#16837766 | C2 | semidirect |
| 3. #21423392 | C2 | direct (N × H) |
| 4. C2×#16837143 | C2 | semidirect |
| 5. C2×#16837142 | C2 | semidirect |
| 9. #16838152 | C22 | semidirect |
| 16. #16837766 | C22 | semidirect |
| 20. #16837143 | C22 | semidirect |
| 21. #16837142 | C22 | semidirect |
| 179. C2×C59 | #1657 | semidirect |
| 204. C59 | C2×#1657 | semidirect |
| 348. C2 | #21423392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838152 | 2 |
| C2×#16837766 | 2 |
| #21423392 | 2 |
| C2×#16837143 | 2 |
| C2×#16837142 | 2 |
| C2×C59×#496 | 2 |
| C2×#1657 | 59 |