Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
602 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21434128 | C2 | semidirect |
| 3. #21429450 | C2 | semidirect |
| 4. #21422657 | C2 | semidirect |
| 5. #21422526 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#1478 | C2 | semidirect |
| 90. C2×D4×C59 | SD16 | semidirect |
| 231. #1478 | D59 | semidirect |
| 265. C59 | #9998 | semidirect |
| 335. C2×D4 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434128 | 2 |
| #21433560 | 2 |
| #21429450 | 2 |
| #21422657 | 2 |
| #21422526 | 2 |
| #21421955 | 2 |
| C59×#1478 | 2 |
| #9998 | 59 |