Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
310 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 310 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 | #124×C197 | C2 |
| hypercenter | #124 | D197 |
| hypocenter | C197 | #532 |
| LCS | G ▷ C22×C197 ▷ C197 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15691359 | C2 | semidirect |
| 2. C2×#15691357 | C2 | semidirect |
| 3. #20263324 | C2 | semidirect |
| 4. #20263322 | C2 | semidirect |
| 5. #20263314 | C2 | semidirect |
| 6. #20263299 | C2 | semidirect |
| 7. #20263286 | C2 | semidirect |
| 8. C42×D197 | C2 | semidirect |
| 9. #124×C197 | C2 | semidirect |
| 42. C4×D197 | D4 | semidirect |
| 61. Dic197 | #41 | semidirect |
| 67. C197 | #532 | semidirect |
| 74. #124 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691359 | 2 |
| C2×#15691357 | 2 |
| #20263324 | 2 |
| #20263322 | 2 |
| #20263314 | 2 |
| #20263299 | 2 |
| #20263286 | 2 |
| C42×D197 | 2 |
| #124×C197 | 2 |
| #532 | 197 |