Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3994 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3994 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#16837547 | C2 | semidirect |
| 2. C2×#16837536 | C2 | semidirect |
| 3. #21429820 | C2 | semidirect |
| 4. #21424036 | C2 | semidirect |
| 5. #21424027 | C2 | semidirect |
| 6. #21424008 | C2 | semidirect |
| 7. C22×H(5,𝔽2)×C59 | C2 | semidirect |
| 8. C22×#11745671 | C22 | semidirect |
| 9. C22×#11745669 | C22 | semidirect |
| 10. C2×#14273701 | C22 | semidirect |
| 13. C2×#14273651 | C22 | semidirect |
| 14. C2×#14273648 | C22 | semidirect |
| 15. C2×#14273648 | C22 | semidirect |
| 16. C2×C22⋊(C59⋊C8) | C22 | semidirect |
| 17. C2×C22⋊(C59⋊C8) | C22 | semidirect |
| 20. #16837262 | C22 | semidirect |
| 55. C2×#41×C59 | D4 | semidirect |
| 66. C22×D4×C59 | D4 | semidirect |
| 191. C22×H(5,𝔽2) | D59 | semidirect |
| 224. C59 | #32884 | semidirect |
| 234. C2×#41 | C22⋊D59 | semidirect |
| 247. C22×D4 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837547 | 2 |
| C2×#16837536 | 2 |
| #21429820 | 2 |
| #21424036 | 2 |
| #21424027 | 2 |
| #21424008 | 2 |
| C22×H(5,𝔽2)×C59 | 2 |
| #32884 | 59 |