Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3067 | C2 | semidirect |
| 2. #83894 | C2 | semidirect |
| 3. #83800 | C2 | semidirect |
| 4. C2×#4566 | C2 | semidirect |
| 5. #72006 | C2 | semidirect |
| 6. #70690 | C2 | semidirect |
| 7. #67730 | C2 | semidirect |
| 35. #3067 | D3 | semidirect |
| 53. C2×C3×Q16 | D4 | semidirect |
| 55. C2×C3×D8 | D4 | semidirect |
| 79. C3×#108 | D4 | semidirect |
| 95. C2×C3⋊C16 | D4 | semidirect |
| 204. C2×Q16 | #67 | semidirect |
| 208. C2×D8 | #67 | semidirect |
| 235. #108 | #67 | semidirect |
| 445. C3 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3067 | 2 |
| #83894 | 2 |
| #83800 | 2 |
| C2×#4566 | 2 |
| #72006 | 2 |
| #70690 | 2 |
| #67730 | 2 |
| #13318 | 3 |