Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D101 |
| commutator, socle, cosocle | C22×C101 | C25 |
| Frattini | C22 | C24×D101 |
| Fitting | C22×C42×C101 | C2 |
| hypercenter | C22×C42 | D101 |
| hypocenter | C101 | #3444 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20265734 | C2 | semidirect |
| 2. #20265727 | C2 | semidirect |
| 3. #20265711 | C2 | semidirect |
| 4. #20265688 | C2 | semidirect |
| 5. C4×#13108074 | C2 | semidirect |
| 6. C22×C42×C101 | C2 | semidirect |
| 8. #15692255 | C22 | semidirect |
| 9. #15692252 | C22 | semidirect |
| 10. #15692249 | C22 | semidirect |
| 11. #15692247 | C22 | semidirect |
| 12. #15692243 | C22 | semidirect |
| 17. C4×Dic202 | C22 | semidirect |
| 18. C4×D404 | C22 | semidirect |
| 21. #15692212 | C22 | semidirect |
| 22. C42×D101 | C22 | semidirect |
| 55. C2×C4×C101 | #41 | semidirect |
| 77. C101 | #3444 | semidirect |
| 83. C22×C42 | D101 | semidirect |
| 137. C2×C4 | #13108074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265734 | 2 |
| #20265727 | 2 |
| #20265711 | 2 |
| #20265688 | 2 |
| C4×#13108074 | 2 |
| C22×C42×C101 | 2 |
| #3444 | 101 |