Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #20260843 | C2 | semidirect |
| 4. #20260842 | C2 | semidirect |
| 5. #20260841 | C2 | semidirect |
| 6. C4×#13095501 | C2 | semidirect |
| 7. #20260827 | C2 | semidirect |
| 11. #441×C97 | C2 | semidirect |
| 15. Q16×D97 | C4 | semidirect |
| 109. C97 | #2950 | semidirect |
| 115. #441 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| #20261211 | 2 |
| #20260843 | 2 |
| #20260842 | 2 |
| #20260841 | 2 |
| C4×#13095501 | 2 |
| #20260827 | 2 |
| #20260770 | 2 |
| #20260742 | 2 |
| #20260692 | 2 |
| #441×C97 | 2 |
| #2950 | 97 |