Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21426321 | C2 | semidirect |
| 3. #21423456 | C2 | semidirect |
| 4. #21422151 | C2 | semidirect |
| 5. Q8⋊(C59⋊C16) | C2 | semidirect |
| 6. #21422057 | C2 | semidirect |
| 7. Q8×D8×C59 | C2 | semidirect |
| 65. D8×C59 | SD16 | semidirect |
| 92. Q8×C59 | D16 | semidirect |
| 132. Q8×D8 | D59 | semidirect |
| 161. C59 | #12352 | semidirect |
| 206. D8 | #11745671 | semidirect |
| 229. Q8 | #14273668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426321 | 2 |
| #21426131 | 2 |
| #21423456 | 2 |
| #21422151 | 2 |
| Q8⋊(C59⋊C16) | 2 |
| #21422057 | 2 |
| Q8×D8×C59 | 2 |
| #12352 | 59 |