Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
270 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 162 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×C109 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C109 |
| prime radical | C2×#41×C109 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Q8×C109 | C2 | semidirect |
| 3. C4⋊Q8×C109 | C2 | semidirect |
| 4. #124×C109 | C2 | semidirect |
| 5. #123×C109 | C2 | semidirect |
| 6. C22⋊Q8×C109 | C2 | semidirect |
| 7. #117×C109 | C2 | semidirect |
| 52. C109 | #536 | direct (N × H) |
| 53. #536 | C109 | direct (N × H) |
| 55. C22×Q8 | C2×C109 | semidirect |
| 56. C4⋊Q8 | C2×C109 | semidirect |
| 57. #124 | C2×C109 | semidirect |
| 58. #123 | C2×C109 | semidirect |
| 59. C22⋊Q8 | C2×C109 | semidirect |
| 60. #117 | C2×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C109 | 2 |
| C22×Q8×C109 | 2 |
| C4⋊Q8×C109 | 2 |
| #124×C109 | 2 |
| #123×C109 | 2 |
| C22⋊Q8×C109 | 2 |
| #117×C109 | 2 |
| #536 | 109 |