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. #20261140 | C2 | semidirect |
| 3. #20261139 | C2 | semidirect |
| 4. #20261138 | C2 | semidirect |
| 7. #500×C97 | C2 | semidirect |
| 32. C8×D97 | Q8 | semidirect |
| 61. C8×C97 | C2×Q8 | semidirect |
| 62. #11715895 | C2×Q8 | semidirect |
| 78. D97 | #500 | direct (N × H) |
| 80. C97 | C2×#500 | semidirect |
| 85. #500 | D97 | direct (N × H) |
| 142. 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 |
| #20261140 | 2 |
| #20261139 | 2 |
| #20261138 | 2 |
| #107×D97 | 2 |
| C4×C8×D97 | 2 |
| #500×C97 | 2 |
| C2×#500 | 97 |