Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21422982 | C2 | semidirect |
| 3. #21422168 | C2 | semidirect |
| 4. #21422058 | C2 | semidirect |
| 5. C8×C16×C59 | C2 | semidirect |
| 46. C16×C59 | M16 | semidirect |
| 59. C8×C59 | D16 | semidirect |
| 78. C8×C16 | D59 | semidirect |
| 93. C59 | #12081 | semidirect |
| 124. C16 | #11745659 | semidirect |
| 138. C8 | D944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D944 | 2 |
| #21422982 | 2 |
| #21422168 | 2 |
| #21422058 | 2 |
| C8×C16×C59 | 2 |
| #12081 | 59 |