Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 111 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. C3×C5×C8×Q8 | C2 | semidirect |
| 2. #11751128 | C2 | semidirect |
| 4. #11746306 | C2 | semidirect |
| 5. #11746279 | C2 | semidirect |
| 19. C5×C8×Q8 | D3 | semidirect |
| 39. C3×C8×Q8 | D5 | semidirect |
| 58. C3×C5×Q8 | D8 | semidirect |
| 71. C3×C5×C8 | SD16 | semidirect |
| 101. C8×Q8 | D15 | semidirect |
| 132. C5×Q8 | D24 | semidirect |
| 145. C5×C8 | #215 | semidirect |
| 164. C3×Q8 | D40 | semidirect |
| 177. C3×C8 | #688 | semidirect |
| 205. C3×C5 | #1668 | semidirect |
| 223. Q8 | D120 | semidirect |
| 237. C8 | #6717 | semidirect |
| 242. C5 | #70939 | semidirect |
| 254. C3 | #10601732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C8×Q8 | 2 |
| #11751128 | 2 |
| #11750796 | 2 |
| #11746306 | 2 |
| #11746279 | 2 |
| #10601732 | 3 |
| #70939 | 5 |