Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 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 |
|---|---|---|
| 88. M16×C59 | Q16 | semidirect |
| 208. C59 | #10199 | semidirect |
| 268. M16 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435438 | 2 |
| #21435044 | 2 |
| #21425045 | 2 |
| #21425040 | 2 |
| #21422595 | 2 |
| #21421947 | 2 |
| C59×#3165 | 2 |
| #10199 | 59 |