Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #21424884 | C2 | semidirect |
| 5. #21422207 | C2 | semidirect |
| 6. #21422184 | C2 | semidirect |
| 7. C2×C59×#368 | C2 | semidirect |
| 17. #16837210 | C4 | semidirect |
| 137. C2×#368 | D59 | semidirect |
| 164. C59 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433012 | 2 |
| #21425823 | 2 |
| C2×#16837210 | 2 |
| #21424884 | 2 |
| #21422207 | 2 |
| #21422184 | 2 |
| C2×C59×#368 | 2 |
| #12947 | 59 |