Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20260488 | C2 | semidirect |
| 4. #20260487 | C2 | semidirect |
| 5. #335×C97 | C2 | semidirect |
| 25. C8×D97 | C8 | semidirect |
| 47. C8×C97 | C2×C8 | semidirect |
| 50. #11715895 | C2×C8 | semidirect |
| 66. D97 | #335 | direct (N × H) |
| 68. C97 | C2×#335 | semidirect |
| 73. #335 | D97 | direct (N × H) |
| 118. C8 | C8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊C8×D97 | 2 |
| C4×C8×D97 | 2 |
| #20260488 | 2 |
| #20260487 | 2 |
| #335×C97 | 2 |
| C2×#335 | 97 |