Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 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. #21432733 | C2 | semidirect |
| 3. #21422765 | C2 | semidirect |
| 4. #21422763 | C2 | semidirect |
| 5. #21422408 | C2 | semidirect |
| 6. #21421954 | C2 | semidirect |
| 7. C59×#1286 | C2 | semidirect |
| 55. C4⋊(C59⋊C8) | D4 | semidirect |
| 66. C4⋊C8×C59 | D4 | semidirect |
| 216. #1286 | D59 | semidirect |
| 245. C59 | #9198 | semidirect |
| 278. C4⋊C8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432733 | 2 |
| #21429849 | 2 |
| #21422765 | 2 |
| #21422763 | 2 |
| #21422408 | 2 |
| #21421954 | 2 |
| C59×#1286 | 2 |
| #9198 | 59 |