Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D197 |
| commutator, socle, cosocle | C22×C197 | C24 |
| Fitting | C4⋊Q8×C197 | C2 |
| hypercenter | C4⋊Q8 | D197 |
| hypocenter | C197 | #547 |
| LCS | G ▷ C22×C197 ▷ C197 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15691359 | C2 | semidirect |
| 2. #20263311 | C2 | semidirect |
| 3. #20263302 | C2 | semidirect |
| 4. #20263301 | C2 | semidirect |
| 5. C4×D788 | C2 | semidirect |
| 6. C4×D788 | C2 | semidirect |
| 7. C4⋊C4×D197 | C2 | semidirect |
| 8. C4⋊Q8×C197 | C2 | semidirect |
| 30. D788 | D4 | semidirect |
| 51. C4×C197 | #41 | semidirect |
| 59. C197 | #547 | semidirect |
| 62. C4⋊Q8 | D197 | semidirect |
| 113. C4 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691359 | 2 |
| #20263311 | 2 |
| #20263302 | 2 |
| #20263301 | 2 |
| C4×D788 | 2 |
| C4⋊C4×D197 | 2 |
| C4⋊Q8×C197 | 2 |
| #547 | 197 |