Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21435282 | C2 | semidirect |
| 3. #21423405 | C2 | semidirect |
| 4. #21423392 | C2 | semidirect |
| 5. #21422720 | C2 | semidirect |
| 6. #21422697 | C2 | semidirect |
| 16. #16837808 | C22 | semidirect |
| 17. #16837766 | C22 | semidirect |
| 22. #16837143 | C22 | semidirect |
| 218. C59 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838152 | 2 |
| #21435282 | 2 |
| #21423405 | 2 |
| #21423392 | 2 |
| #21422720 | 2 |
| #21422697 | 2 |
| C59×#3153 | 2 |
| #18994 | 59 |