Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
528 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 167 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. #21426321 | C2 | semidirect |
| 3. #21426240 | C2 | semidirect |
| 4. #21426136 | C2 | semidirect |
| 5. Q8×C59⋊C16 | C2 | semidirect |
| 6. C4×#14273670 | C2 | semidirect |
| 7. Q8×Q16×C59 | C2 | semidirect |
| 55. Q16×C59 | #41 | semidirect |
| 75. Q8×C59 | SD32 | semidirect |
| 103. Q8×Q16 | D59 | semidirect |
| 129. C59 | #33929 | semidirect |
| 161. Q16 | #11745689 | semidirect |
| 181. Q8 | #14273670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437071 | 2 |
| #21426321 | 2 |
| #21426240 | 2 |
| #21426136 | 2 |
| Q8×C59⋊C16 | 2 |
| C4×#14273670 | 2 |
| Q8×Q16×C59 | 2 |
| #33929 | 59 |