Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. #20261292 | C2 | semidirect |
| 3. #20261133 | C2 | semidirect |
| 4. #20261108 | C2 | semidirect |
| 5. #20261086 | C2 | semidirect |
| 6. #20261082 | C2 | semidirect |
| 7. #20260964 | C2 | semidirect |
| 8. C4×#13095500 | C2 | semidirect |
| 9. C2×C4×C8×C97 | C2 | semidirect |
| 71. C2×C4×C97 | SD16 | semidirect |
| 90. C8×C97 | #41 | semidirect |
| 113. C97 | #3167 | semidirect |
| 122. C2×C4×C8 | D97 | semidirect |
| 195. C2×C4 | #13095500 | semidirect |
| 203. C8 | #13095511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261292 | 2 |
| #20261285 | 2 |
| #20261133 | 2 |
| #20261108 | 2 |
| #20261086 | 2 |
| #20261082 | 2 |
| #20260964 | 2 |
| C4×#13095500 | 2 |
| C2×C4×C8×C97 | 2 |
| #3167 | 97 |