Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 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. #21437071 | C2 | semidirect |
| 2. Q8×D472 | C2 | semidirect |
| 3. #21426320 | C2 | semidirect |
| 4. #21426234 | C2 | semidirect |
| 5. #21426132 | C2 | semidirect |
| 6. C4×D944 | C2 | semidirect |
| 7. Q8×C16×C59 | C2 | semidirect |
| 69. D472 | #41 | semidirect |
| 74. Q8×C59 | D16 | semidirect |
| 111. Q8×C16 | D59 | semidirect |
| 134. C59 | #33925 | semidirect |
| 186. Q8 | D944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437071 | 2 |
| Q8×D472 | 2 |
| #21426320 | 2 |
| #21426234 | 2 |
| #21426132 | 2 |
| C4×D944 | 2 |
| Q8×C16×C59 | 2 |
| #33925 | 59 |