Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3876 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 3876 conjugacy classes of subgroups — too many to draw. Only its 387 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×#16837541 | C2 | semidirect |
| 3. #21424031 | C2 | semidirect |
| 4. #21424006 | C2 | semidirect |
| 5. C24×Q8×C59 | C2 | semidirect |
| 6. C22×#11745671 | C22 | semidirect |
| 10. C2×#14273651 | C22 | semidirect |
| 38. C22×Q8×C59 | D4 | semidirect |
| 47. C24×C59 | SD16 | semidirect |
| 92. Q8×C59 | #120 | semidirect |
| 112. C22×C59 | #448 | semidirect |
| 123. C24×Q8 | D59 | semidirect |
| 146. C59 | #32879 | semidirect |
| 154. C22×Q8 | C22⋊D59 | semidirect |
| 176. C24 | #11745671 | semidirect |
| 220. Q8 | #14273696 | semidirect |
| 242. C22 | #16837541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837541 | 2 |
| #21432378 | 2 |
| #21424031 | 2 |
| #21424006 | 2 |
| C24×Q8×C59 | 2 |
| #32879 | 59 |