Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 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. C2×#5193 | C2 | semidirect |
| 3. #83799 | C2 | semidirect |
| 4. #72076 | C2 | semidirect |
| 5. #72006 | C2 | semidirect |
| 6. C2×#4495 | C2 | semidirect |
| 7. #67735 | C2 | semidirect |
| 33. #3067 | D3 | semidirect |
| 51. C2×C3×Q16 | D4 | semidirect |
| 53. C2×C3×D8 | D4 | semidirect |
| 75. C3×#108 | D4 | semidirect |
| 86. #812 | D4 | semidirect |
| 185. C2×Q16 | #67 | semidirect |
| 193. C2×D8 | #67 | semidirect |
| 217. #108 | #67 | semidirect |
| 415. C3 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3067 | 2 |
| C2×#5193 | 2 |
| #83799 | 2 |
| #72076 | 2 |
| #72006 | 2 |
| C2×#4495 | 2 |
| #67735 | 2 |
| #13310 | 3 |