Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425073 | C2 | semidirect |
| 3. #21424248 | C2 | semidirect |
| 4. #21422787 | C2 | semidirect |
| 6. #21421970 | C2 | semidirect |
| 99. C42×C59 | SD16 | semidirect |
| 219. C59 | #10520 | semidirect |
| 306. C42 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435412 | 2 |
| #21425073 | 2 |
| #21424248 | 2 |
| #21422787 | 2 |
| #21422773 | 2 |
| #21421970 | 2 |
| C59×#1962 | 2 |
| #10520 | 59 |