Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
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×#20259458 | C2 | semidirect |
| 2. C2×#20259456 | C2 | semidirect |
| 3. #27133862 | C2 | direct (N × H) |
| 4. C2×#20259447 | C2 | semidirect |
| 5. C2×#20259446 | C2 | semidirect |
| 6. C2×#20259442 | C2 | semidirect |
| 7. C2×C8×D383 | C2 | semidirect |
| 8. C2×SD16×C383 | C2 | semidirect |
| 10. #20259458 | C22 | semidirect |
| 12. #20259456 | C22 | semidirect |
| 20. #20259447 | C22 | semidirect |
| 21. #20259446 | C22 | semidirect |
| 22. #20259442 | C22 | semidirect |
| 24. C8×D383 | C22 | semidirect |
| 27. SD16×C383 | C22 | semidirect |
| 65. C2×C383 | #135 | semidirect |
| 69. C383 | C2×#135 | semidirect |
| 76. C2×SD16 | D383 | semidirect |
| 94. SD16 | C2×D383 | semidirect |
| 137. C2 | #27133862 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259458 | 2 |
| C2×#20259456 | 2 |
| #27133862 | 2 |
| C2×#20259447 | 2 |
| C2×#20259446 | 2 |
| C2×#20259442 | 2 |
| C2×C8×D383 | 2 |
| C2×SD16×C383 | 2 |
| C2×#135 | 383 |