Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #20260559 | C2 | semidirect |
| 5. #20260558 | C2 | semidirect |
| 6. #20260557 | C2 | semidirect |
| 7. #365×C97 | C2 | semidirect |
| 12. #15690749 | C4 | semidirect |
| 13. C16×D97 | C4 | semidirect |
| 33. #13095486 | C2×C4 | semidirect |
| 37. C16×C97 | C2×C4 | semidirect |
| 67. D97 | #365 | direct (N × H) |
| 69. C97 | C2×#365 | semidirect |
| 76. #365 | D97 | direct (N × H) |
| 106. C16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D97 | 2 |
| #108×D97 | 2 |
| #106×D97 | 2 |
| #20260559 | 2 |
| #20260558 | 2 |
| #20260557 | 2 |
| #365×C97 | 2 |
| C2×#365 | 97 |