Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
278 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 50 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. #88740 | C2 | semidirect |
| 2. C2×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. #3748⋊C3 | C2 | semidirect |
| 4. #88438 | C2 | semidirect |
| 5. #88436 | C2 | semidirect |
| 11. C4⋊#272 | C22 | semidirect |
| 13. #6229 | C22 | semidirect |
| 16. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 17. C2×C4⋊(C3⋊D3) | D3 | semidirect |
| 22. #3748 | D3 | semidirect |
| 59. C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 101. H(3,𝔽3) | AGL(1,ℤ/8) | semidirect |
| 177. C32 | #908 | semidirect |
| 178. C32 | #932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88740 | 2 |
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| #3748⋊C3 | 2 |
| #88438 | 2 |
| #88436 | 2 |
| #63825 | 3 |
| #63823 | 3 |