Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. #21432478 | C2 | semidirect |
| 2. #21432463 | C2 | semidirect |
| 3. #21432411 | C2 | semidirect |
| 4. C4×#14273721 | C2 | semidirect |
| 6. #21426579 | C2 | semidirect |
| 7. C2×C43×C59 | C2 | semidirect |
| 65. C42×C59 | #41 | semidirect |
| 79. C2×C4×C59 | #126 | semidirect |
| 108. C2×C43 | D59 | semidirect |
| 130. C59 | #36641 | semidirect |
| 176. C42 | #11745685 | semidirect |
| 192. C2×C4 | #14273721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432478 | 2 |
| #21432463 | 2 |
| #21432411 | 2 |
| C4×#14273721 | 2 |
| #21426586 | 2 |
| #21426579 | 2 |
| C2×C43×C59 | 2 |
| #36641 | 59 |