Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1419 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×C4⋊#272 | C2 | semidirect |
| 2. C22×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C22×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 4. C2×#88436 | C2 | direct (N × H) |
| 11. C2×C4⋊#272 | C22 | semidirect |
| 13. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 14. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 15. #88436 | C22 | direct (N × H) |
| 16. C22×C4⋊(C3⋊D3) | D3 | semidirect |
| 21. C22×C3⋊(C3⋊C8) | D3 | semidirect |
| 33. C4⋊#272 | C23 | semidirect |
| 35. C4⋊((C3⋊D3)⋊C3) | C23 | semidirect |
| 36. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 49. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 58. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 62. C22×H(3,𝔽3) | D8 | semidirect |
| 103. C4⋊(C3⋊D3) | C22×D3 | semidirect |
| 112. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 115. C2×H(3,𝔽3) | C2×D8 | semidirect |
| 152. C22×C32 | D24 | semidirect |
| 153. C22×C32 | #213 | semidirect |
| 176. H(3,𝔽3) | C22×D8 | semidirect |
| 222. C2×C32 | C2×D24 | semidirect |
| 223. C2×C32 | C2×#213 | semidirect |
| 271. C32 | C22×D24 | semidirect |
| 272. C32 | C22×#213 | semidirect |
| 304. C22 | #88436 | direct (N × H) |
| 314. C2 | C2×#88436 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| C22×C4⋊((C3⋊D3)⋊C3) | 2 |
| C22×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×#88436 | 2 |
| C22×#3714 | 3 |
| C22×#3713 | 3 |