Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21425890 | C2 | semidirect |
| 4. #21424847 | C2 | semidirect |
| 5. #21422211 | C2 | semidirect |
| 6. #21422179 | C2 | semidirect |
| 18. #16837212 | C4 | semidirect |
| 167. C59 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837524 | 2 |
| #21425890 | 2 |
| #21425832 | 2 |
| #21424847 | 2 |
| #21422211 | 2 |
| #21422179 | 2 |
| C59×#2143 | 2 |
| #12944 | 59 |