Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 3. #21434642 | C2 | semidirect |
| 4. #21425018 | C2 | semidirect |
| 6. #21422596 | C2 | semidirect |
| 7. C59×#1283 | C2 | semidirect |
| 97. M16×C59 | SD16 | semidirect |
| 191. #1283 | D59 | semidirect |
| 221. C59 | #10201 | semidirect |
| 289. M16 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435413 | 2 |
| #21435226 | 2 |
| #21434642 | 2 |
| #21425018 | 2 |
| #21425015 | 2 |
| #21422596 | 2 |
| C59×#1283 | 2 |
| #10201 | 59 |