Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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. #21437061 | C2 | semidirect |
| 4. #21422147 | C2 | semidirect |
| 5. #21422077 | C2 | semidirect |
| 6. #21422066 | C2 | semidirect |
| 68. Q16×C59 | SD16 | semidirect |
| 166. C59 | #12361 | semidirect |
| 208. Q16 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437061 | 2 |
| #21426337 | 2 |
| #21423577 | 2 |
| #21422147 | 2 |
| #21422077 | 2 |
| #21422066 | 2 |
| C59×#2207 | 2 |
| #12361 | 59 |