Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11751108 | C2 | semidirect |
| 3. #11747077 | C2 | semidirect |
| 4. #11746906 | C2 | semidirect |
| 5. C3×D4⋊#168 | C2 | semidirect |
| 6. #11745853 | C2 | semidirect |
| 7. #11745837 | C2 | semidirect |
| 12. #91758 | C22 | semidirect |
| 21. C4⋊(C3⋊#168) | C22 | semidirect |
| 22. C3×C4⋊#168 | C22 | semidirect |
| 23. C3×C4×#168 | C22 | semidirect |
| 33. D4⋊#168 | D3 | semidirect |
| 83. C4⋊#168 | C2×D3 | semidirect |
| 84. C4×#168 | C2×D3 | semidirect |
| 93. C3×C5×D4 | SD16 | semidirect |
| 231. C5×D4 | #204 | semidirect |
| 277. C3×D4 | #687 | semidirect |
| 348. C3×C5 | #1639 | semidirect |
| 392. D4 | #6659 | semidirect |
| 412. C5 | #68182 | semidirect |
| 432. C3 | #10602701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×D12 | 2 |
| #11751108 | 2 |
| #11747077 | 2 |
| #11746906 | 2 |
| C3×D4⋊#168 | 2 |
| #11745853 | 2 |
| #11745837 | 2 |
| #10602701 | 3 |
| #68182 | 5 |