Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
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×#10596966 | C2 | semidirect |
| 2. C2×#10596964 | C2 | semidirect |
| 3. #11924557 | C2 | direct (N × H) |
| 4. C2×#10596942 | C2 | semidirect |
| 5. C2×#10596930 | C2 | semidirect |
| 6. C2×#10596939 | C2 | semidirect |
| 7. C2×C8×D37 | C2 | semidirect |
| 8. C2×SD16×C37 | C2 | semidirect |
| 14. #10596966 | C22 | semidirect |
| 16. #10596964 | C22 | semidirect |
| 22. SD16×C37 | C22 | semidirect |
| 24. #10596942 | C22 | semidirect |
| 25. #10596939 | C22 | semidirect |
| 27. #10596930 | C22 | semidirect |
| 28. C8×D37 | C22 | semidirect |
| 65. C2×C37 | #135 | semidirect |
| 70. C37 | C2×#135 | semidirect |
| 76. C2×SD16 | D37 | semidirect |
| 94. SD16 | C2×D37 | semidirect |
| 137. C2 | #11924557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596966 | 2 |
| C2×#10596964 | 2 |
| #11924557 | 2 |
| C2×#10596942 | 2 |
| C2×#10596930 | 2 |
| C2×#10596939 | 2 |
| C2×C8×D37 | 2 |
| C2×SD16×C37 | 2 |
| C2×#135 | 37 |