Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
190 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16838749 | C2 | semidirect |
| 5. #21440549 | C2 | semidirect |
| 6. #21440549 | C2 | semidirect |
| 7. C2×C42×C241 | C2 | semidirect |
| 15. #16838747 | C4 | semidirect |
| 74. C241 | #388 | semidirect |
| 80. C2×C42 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838749 | 2 |
| C2×#16838747 | 2 |
| #21440549 | 2 |
| C2×C42×C241 | 2 |
| #388 | 241 |