Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #21423466 | C2 | semidirect |
| 4. #21422170 | C2 | semidirect |
| 5. #21422146 | C2 | semidirect |
| 7. Q8×C16×C59 | C2 | semidirect |
| 70. C16×C59 | SD16 | semidirect |
| 73. Q8×C59 | SD32 | semidirect |
| 107. Q8×C16 | D59 | semidirect |
| 132. C59 | #12441 | semidirect |
| 180. C16 | #11745671 | semidirect |
| 185. Q8 | #14273672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426352 | 2 |
| #21423466 | 2 |
| #21423456 | 2 |
| #21422170 | 2 |
| #21422146 | 2 |
| #21422143 | 2 |
| Q8×C16×C59 | 2 |
| #12441 | 59 |