Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21422061 | C2 | semidirect |
| 5. #21422060 | C2 | semidirect |
| 6. #21422059 | C2 | semidirect |
| 7. C59×#1332 | C2 | semidirect |
| 73. Q16×C59 | M16 | semidirect |
| 97. Dic236 | M16 | semidirect |
| 157. #1332 | D59 | semidirect |
| 181. C59 | #11658 | semidirect |
| 231. Q16 | #11745659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D59 | 2 |
| #21425893 | 2 |
| #21422853 | 2 |
| #21422061 | 2 |
| #21422060 | 2 |
| #21422059 | 2 |
| C59×#1332 | 2 |
| #11658 | 59 |