Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 90. M16×C59 | Q16 | semidirect |
| 210. C59 | #10203 | semidirect |
| 271. M16 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435438 | 2 |
| #21435247 | 2 |
| #21425040 | 2 |
| #21425020 | 2 |
| #21422595 | 2 |
| #21421947 | 2 |
| C59×#3165 | 2 |
| #10203 | 59 |