Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15691887 | C2 | semidirect |
| 2. C2×#15691885 | C2 | semidirect |
| 3. #20263976 | C2 | direct (N × H) |
| 4. C2×#15691876 | C2 | semidirect |
| 5. C2×#15691875 | C2 | semidirect |
| 6. C2×#15691871 | C2 | semidirect |
| 7. C2×C8×D199 | C2 | semidirect |
| 8. C2×SD16×C199 | C2 | semidirect |
| 10. #15691887 | C22 | semidirect |
| 12. #15691885 | C22 | semidirect |
| 20. #15691876 | C22 | semidirect |
| 21. #15691875 | C22 | semidirect |
| 22. #15691871 | C22 | semidirect |
| 24. C8×D199 | C22 | semidirect |
| 27. SD16×C199 | C22 | semidirect |
| 65. C2×C199 | #135 | semidirect |
| 69. C199 | C2×#135 | semidirect |
| 76. C2×SD16 | D199 | semidirect |
| 94. SD16 | C2×D199 | semidirect |
| 137. C2 | #20263976 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691887 | 2 |
| C2×#15691885 | 2 |
| #20263976 | 2 |
| C2×#15691876 | 2 |
| C2×#15691875 | 2 |
| C2×#15691871 | 2 |
| C2×C8×D199 | 2 |
| C2×SD16×C199 | 2 |
| C2×#135 | 199 |