Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
602 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21433136 | C2 | semidirect |
| 3. #21424085 | C2 | semidirect |
| 4. #21422522 | C2 | semidirect |
| 5. #21422520 | C2 | semidirect |
| 6. #21421954 | C2 | semidirect |
| 7. C59×#1286 | C2 | semidirect |
| 56. C4×C59⋊C8 | D4 | semidirect |
| 65. C4×C8×C59 | D4 | semidirect |
| 209. #1286 | D59 | semidirect |
| 236. C59 | #9489 | semidirect |
| 274. C4×C8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433136 | 2 |
| #21428998 | 2 |
| #21424085 | 2 |
| #21422522 | 2 |
| #21422520 | 2 |
| #21421954 | 2 |
| C59×#1286 | 2 |
| #9489 | 59 |