Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 188 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.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C109 |
| prime radical | C22×D4×C109 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×SD16×C109 | C2 | semidirect |
| 3. C22⋊Q8×C109 | C2 | semidirect |
| 4. #102×C109 | C2 | semidirect |
| 5. C22⋊C8×C109 | C2 | semidirect |
| 7. C2×Q8×C109 | C22 | semidirect |
| 13. C2×C8×C109 | C22 | semidirect |
| 15. C4⋊C4×C109 | C22 | semidirect |
| 38. C22×C109 | SD16 | semidirect |
| 49. C109 | #450 | direct (N × H) |
| 50. #450 | C109 | direct (N × H) |
| 52. C2×SD16 | C2×C109 | semidirect |
| 53. C22⋊Q8 | C2×C109 | semidirect |
| 54. #102 | C2×C109 | semidirect |
| 55. C22⋊C8 | C2×C109 | semidirect |
| 57. C2×Q8 | C22×C109 | semidirect |
| 63. C2×C8 | C22×C109 | semidirect |
| 65. C4⋊C4 | C22×C109 | semidirect |
| 88. C22 | SD16×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C109 | 2 |
| C2×SD16×C109 | 2 |
| C22⋊Q8×C109 | 2 |
| #102×C109 | 2 |
| C22⋊C8×C109 | 2 |
| #450 | 109 |