Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
528 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #20260490 | C2 | semidirect |
| 4. #20260489 | C2 | semidirect |
| 5. #336×C97 | C2 | semidirect |
| 11. C2×C8×D97 | C4 | semidirect |
| 22. C2×C4×D97 | C8 | semidirect |
| 29. C2×#11715895 | C2×C4 | semidirect |
| 37. C2×C8×C97 | C2×C4 | semidirect |
| 47. C2×C4×C97 | C2×C8 | semidirect |
| 57. C2×Dic97 | C2×C8 | semidirect |
| 83. D97 | #336 | direct (N × H) |
| 85. C97 | C2×#336 | semidirect |
| 90. #336 | D97 | direct (N × H) |
| 120. C2×C8 | C4×D97 | semidirect |
| 141. C2×C4 | C8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D97 | 2 |
| C2×C42×D97 | 2 |
| #20260490 | 2 |
| #20260489 | 2 |
| #336×C97 | 2 |
| C2×#336 | 97 |