Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
4854 conjugacy classes of subgroups; only the 807 normal subgroups are shown.
This group has 4854 conjugacy classes of subgroups — too many to draw. Only its 807 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. #21437736 | C2 | semidirect |
| 2. #21433502 | C2 | semidirect |
| 3. #21433493 | C2 | semidirect |
| 4. #21433488 | C2 | semidirect |
| 5. C2×#16837592 | C2 | semidirect |
| 6. #21432557 | C2 | semidirect |
| 7. C59×H(7,𝔽2) | C2 | semidirect |
| 8. C22×#11745687 | C22 | semidirect |
| 11. #16837973 | C22 | semidirect |
| 12. #16837961 | C22 | semidirect |
| 13. #16837909 | C22 | semidirect |
| 14. C2×#14273708 | C22 | semidirect |
| 15. #16837877 | C22 | semidirect |
| 16. #16837592 | C22 | semidirect |
| 17. #16837592 | C22 | semidirect |
| 18. #16837589 | C22 | semidirect |
| 19. #16837376 | C22 | semidirect |
| 20. C2×#14273642 | C22 | semidirect |
| 27. C22×Dic118 | C23 | semidirect |
| 28. C22×C22⋊D59 | C23 | semidirect |
| 29. C23×Dic59 | C23 | semidirect |
| 30. C22×C4×D59 | C23 | semidirect |
| 35. #14273708 | C23 | semidirect |
| 36. #14273708 | C23 | semidirect |
| 42. #14273695 | C23 | semidirect |
| 45. #14273686 | C23 | semidirect |
| 48. C2×C22⋊Dic59 | C23 | semidirect |
| 49. #14273642 | C23 | semidirect |
| 60. C2×#41×C59 | D4 | semidirect |
| 64. C22×D4×C59 | D4 | semidirect |
| 160. H(7,𝔽2) | D59 | semidirect |
| 190. C59 | #60401 | semidirect |
| 202. C2×#41 | C22⋊D59 | semidirect |
| 208. C22×D4 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437736 | 2 |
| #21433502 | 2 |
| #21433493 | 2 |
| #21433488 | 2 |
| C2×#16837592 | 2 |
| #21432557 | 2 |
| C59×H(7,𝔽2) | 2 |
| #60401 | 59 |