Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. #20261133 | C2 | semidirect |
| 3. #20261132 | C2 | semidirect |
| 4. #20261131 | C2 | semidirect |
| 7. #498×C97 | C2 | semidirect |
| 31. C8×D97 | Q8 | semidirect |
| 56. C8×C97 | C2×Q8 | semidirect |
| 57. #11715895 | C2×Q8 | semidirect |
| 69. D97 | #498 | direct (N × H) |
| 71. C97 | C2×#498 | semidirect |
| 76. #498 | D97 | direct (N × H) |
| 128. C8 | Q8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D97 | 2 |
| #20261133 | 2 |
| #20261132 | 2 |
| #20261131 | 2 |
| #106×D97 | 2 |
| C4×C8×D97 | 2 |
| #498×C97 | 2 |
| C2×#498 | 97 |