Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 103 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. Q8×C9×Dic3 | C2 | semidirect |
| 4. C3×#63395 | C2 | semidirect |
| 6. #11720263 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 13. #88548 | C4 | semidirect |
| 33. #63395 | D3 | semidirect |
| 39. C3×Q8×C9 | C2×C4 | semidirect |
| 49. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 93. Q8×Dic3 | D9 | semidirect |
| 126. Q8×C9 | C4×D3 | semidirect |
| 212. C3×C9 | #440 | semidirect |
| 220. C3×Q8 | C4×D9 | semidirect |
| 304. C9 | #4817 | semidirect |
| 307. Q8 | (C3⋊D9)⋊C4 | semidirect |
| 343. C3 | #10588709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| Q8×C9×Dic3 | 2 |
| #11720993 | 2 |
| C3×#63395 | 2 |
| #11720267 | 2 |
| #11720263 | 2 |
| #11720258 | 2 |
| #10591540 | 3 |
| #10588709 | 3 |