Finite Group DatabasebetaFinite Group DatabasebetaOrder 704.
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C11 |
| prime radical | C2×C11×#41 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C11×Q16 | C2 | semidirect |
| 3. C2×C11×SD16 | C2 | semidirect |
| 4. C11×C22⋊Q8 | C2 | semidirect |
| 5. C11×#103 | C2 | semidirect |
| 6. C11×#102 | C2 | semidirect |
| 7. C11×C22⋊C8 | C2 | semidirect |
| 42. #452 | C11 | direct (N × H) |
| 57. C2×Q16 | C2×C11 | semidirect |
| 58. C2×SD16 | C2×C11 | semidirect |
| 59. C22⋊Q8 | C2×C11 | semidirect |
| 60. #103 | C2×C11 | semidirect |
| 61. #102 | C2×C11 | semidirect |
| 62. C22⋊C8 | C2×C11 | semidirect |
| 83. C11 | #452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#41 | 2 |
| C2×C11×Q16 | 2 |
| C2×C11×SD16 | 2 |
| C11×C22⋊Q8 | 2 |
| C11×#103 | 2 |
| C11×#102 | 2 |
| C11×C22⋊C8 | 2 |
| #452 | 11 |