Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20261020 | C2 | semidirect |
| 4. #20260486 | C2 | semidirect |
| 5. #20260482 | C2 | semidirect |
| 7. C8×Q8×C97 | C2 | semidirect |
| 44. Q8×C97 | SD16 | semidirect |
| 60. C8×C97 | SD16 | semidirect |
| 80. C97 | #1666 | semidirect |
| 84. C8×Q8 | D97 | semidirect |
| 126. Q8 | #13095500 | semidirect |
| 142. C8 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261108 | 2 |
| #20261020 | 2 |
| #20260935 | 2 |
| #20260486 | 2 |
| #20260482 | 2 |
| #20260478 | 2 |
| C8×Q8×C97 | 2 |
| #1666 | 97 |