Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
341 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 62 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. #88748 | C2 | semidirect |
| 2. Q16×H(3,𝔽3) | C2 | semidirect |
| 3. #88549 | C2 | semidirect |
| 4. #88529 | C2 | semidirect |
| 5. C8×#272 | C2 | semidirect |
| 15. C32×Q16 | D3 | semidirect |
| 52. H(3,𝔽3) | #135 | semidirect |
| 71. Q16 | #272 | semidirect |
| 85. C32 | #919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88748 | 2 |
| Q16×H(3,𝔽3) | 2 |
| #88549 | 2 |
| #88529 | 2 |
| C8×#272 | 2 |
| C3×#919 | 3 |