Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
694 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #21433137 | C2 | semidirect |
| 2. #21422487 | C2 | semidirect |
| 3. #21422417 | C2 | semidirect |
| 4. #21421929 | C2 | semidirect |
| 23. C4⋊(C59⋊C8) | D4 | semidirect |
| 65. C2×D4×C59 | M16 | semidirect |
| 90. C42×C59 | M16 | semidirect |
| 189. C59 | #8963 | semidirect |
| 234. C2×D4 | #11745664 | semidirect |
| 262. C42 | #11745664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433137 | 2 |
| #21422487 | 2 |
| #21422417 | 2 |
| #21421929 | 2 |
| C4×#127×C59 | 2 |
| #8963 | 59 |