Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D199 |
| commutator, socle, cosocle | C22×C199 | C24 |
| Frattini | C22 | C23×D199 |
| Fitting | C2×#41×C199 | C2 |
| hypercenter | C2×#41 | D199 |
| hypocenter | C199 | #525 |
| LCS | G ▷ C22×C199 ▷ C199 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4×D199 | C2 | semidirect |
| 2. #20263936 | C2 | semidirect |
| 3. #20263931 | C2 | semidirect |
| 4. #20263926 | C2 | semidirect |
| 5. #20263923 | C2 | semidirect |
| 6. C4×C22⋊D199 | C2 | semidirect |
| 7. #20263914 | C2 | semidirect |
| 8. C2×#41×C199 | C2 | semidirect |
| 15. C4⋊Dic199 | C22 | semidirect |
| 16. Dic199⋊C4 | C22 | semidirect |
| 18. C22⋊Dic199 | C22 | semidirect |
| 20. C4×Dic199 | C22 | semidirect |
| 22. C2×Q8×C199 | C22 | semidirect |
| 24. C2×D4×C199 | C22 | semidirect |
| 26. C22×C4×C199 | C22 | semidirect |
| 42. C2×C4×C199 | D4 | semidirect |
| 54. C2×D199 | #41 | semidirect |
| 65. C199 | #525 | semidirect |
| 67. C2×#41 | D199 | semidirect |
| 77. C2×Q8 | C2×D199 | semidirect |
| 80. C2×D4 | C2×D199 | semidirect |
| 86. C22×C4 | C2×D199 | semidirect |
| 108. C2×C4 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D199 | 2 |
| #20263936 | 2 |
| #20263931 | 2 |
| #20263926 | 2 |
| #20263923 | 2 |
| C4×C22⋊D199 | 2 |
| #20263914 | 2 |
| C2×#41×C199 | 2 |
| #525 | 199 |