Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #21425893 | C2 | semidirect |
| 3. #21422853 | C2 | semidirect |
| 4. #21422061 | C2 | semidirect |
| 5. #21422059 | C2 | semidirect |
| 6. #21422057 | C2 | semidirect |
| 7. C59×#1331 | C2 | semidirect |
| 74. D8×C59 | M16 | semidirect |
| 97. Dic236 | M16 | semidirect |
| 161. #1331 | D59 | semidirect |
| 186. C59 | #11660 | semidirect |
| 237. D8 | #11745659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273746 | 2 |
| #21425893 | 2 |
| #21422853 | 2 |
| #21422061 | 2 |
| #21422059 | 2 |
| #21422057 | 2 |
| C59×#1331 | 2 |
| #11660 | 59 |