Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 640 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 |
|---|---|---|
| 1. #21435412 | C2 | semidirect |
| 2. #21435037 | C2 | semidirect |
| 3. #21425040 | C2 | semidirect |
| 4. #21425024 | C2 | semidirect |
| 5. #21422591 | C2 | semidirect |
| 6. #21421947 | C2 | semidirect |
| 107. M16×C59 | SD16 | semidirect |
| 240. C59 | #10194 | semidirect |
| 319. M16 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435412 | 2 |
| #21435037 | 2 |
| #21425040 | 2 |
| #21425024 | 2 |
| #21422591 | 2 |
| #21421947 | 2 |
| C59×#3151 | 2 |
| #10194 | 59 |