Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
512 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 71 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×D8×C3⋊D3 | C2 | semidirect |
| 2. #11723654 | C2 | semidirect |
| 3. C3×#63654 | C2 | semidirect |
| 4. C3×#63653 | C2 | semidirect |
| 5. #11722068 | C2 | semidirect |
| 6. #11722067 | C2 | semidirect |
| 7. #11722066 | C2 | semidirect |
| 15. C3×#3746 | C22 | semidirect |
| 17. C3×#3745 | C22 | semidirect |
| 20. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 21. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 22. D8×C3⋊D3 | D3 | semidirect |
| 29. #63654 | D3 | semidirect |
| 30. #63653 | D3 | semidirect |
| 75. #3746 | C2×D3 | semidirect |
| 77. #3745 | C2×D3 | semidirect |
| 97. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 98. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 281. C33 | #509 | semidirect |
| 409. C32 | #4911 | semidirect |
| 410. C32 | #4914 | semidirect |
| 411. C32 | #5147 | semidirect |
| 461. C3 | #10591031 | semidirect |
| 462. C3 | #10591033 | semidirect |
| 463. C3 | #10591036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D8×C3⋊D3 | 2 |
| #11723654 | 2 |
| C3×#63654 | 2 |
| C3×#63653 | 2 |
| #11722068 | 2 |
| #11722067 | 2 |
| #11722066 | 2 |
| #10591036 | 3 |
| #10591033 | 3 |
| #10591031 | 3 |