Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 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. #21426184 | C2 | direct (N × H) |
| 4. C2×#16837228 | C2 | semidirect |
| 5. C2×#16837206 | C2 | semidirect |
| 6. C22×Q32×C59 | C2 | semidirect |
| 16. #16837228 | C22 | semidirect |
| 17. #16837206 | C22 | semidirect |
| 20. C2×Q32×C59 | C22 | semidirect |
| 82. C22×D59 | Q32 | semidirect |
| 112. C2×D59 | C2×Q32 | semidirect |
| 119. C22×Q32 | D59 | semidirect |
| 125. C2×C59 | #2216 | semidirect |
| 134. C2×Q32 | C2×D59 | semidirect |
| 145. C59 | C2×#2216 | semidirect |
| 243. C2 | #21426184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D59 | 2 |
| C2×#16837640 | 2 |
| #21426184 | 2 |
| C2×#16837228 | 2 |
| C2×#16837206 | 2 |
| C22×Q32×C59 | 2 |
| C2×#2216 | 59 |