Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21425036 | C2 | semidirect |
| 5. #21422526 | C2 | semidirect |
| 6. #21421992 | C2 | semidirect |
| 7. C59×#1281 | C2 | semidirect |
| 96. C2×C8×C59 | SD16 | semidirect |
| 186. #1281 | D59 | semidirect |
| 214. C59 | #9047 | semidirect |
| 291. C2×C8 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434128 | 2 |
| #21432815 | 2 |
| #21425036 | 2 |
| #21422743 | 2 |
| #21422526 | 2 |
| #21421992 | 2 |
| C59×#1281 | 2 |
| #9047 | 59 |