Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1010 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 3. #21423236 | C2 | direct (N × H) |
| 71. C2×Q8×C59 | Q16 | semidirect |
| 109. Q8×C59 | C2×Q16 | semidirect |
| 148. C2×C59 | #1633 | semidirect |
| 171. C59 | C2×#1633 | semidirect |
| 219. C2×Q8 | #11745672 | semidirect |
| 256. Q8 | C2×#11745672 | semidirect |
| 286. C2 | #21423236 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837781 | 2 |
| C2×#16837697 | 2 |
| #21423236 | 2 |
| C2×#16837151 | 2 |
| C2×Q8⋊(C59⋊C8) | 2 |
| C2×Q82×C59 | 2 |
| C2×#1633 | 59 |