Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261101 | C2 | semidirect |
| 3. #20261083 | C2 | semidirect |
| 4. #20260739 | C2 | semidirect |
| 5. C4×#13095495 | C2 | semidirect |
| 6. #533×C97 | C2 | semidirect |
| 13. #15690730 | C22 | semidirect |
| 14. #15690721 | C22 | semidirect |
| 15. C4×#11715895 | C22 | semidirect |
| 16. C4⋊Q8×C97 | C22 | semidirect |
| 17. #125×C97 | C22 | semidirect |
| 75. C97 | #3138 | semidirect |
| 76. #533 | D97 | semidirect |
| 85. C4⋊Q8 | C2×D97 | semidirect |
| 89. #125 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690807 | 2 |
| #20261101 | 2 |
| #20261083 | 2 |
| #20260739 | 2 |
| C4×#13095495 | 2 |
| #533×C97 | 2 |
| #3138 | 97 |