Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×Q16×D97 | C2 | semidirect |
| 3. #20261177 | C2 | direct (N × H) |
| 4. C2×#15690756 | C2 | semidirect |
| 5. C2×#15690755 | C2 | semidirect |
| 6. C2×#15690753 | C2 | semidirect |
| 7. C2×#15690749 | C2 | semidirect |
| 8. C2×Q32×C97 | C2 | semidirect |
| 16. Q16×D97 | C22 | semidirect |
| 20. #15690756 | C22 | semidirect |
| 21. #15690755 | C22 | semidirect |
| 22. #15690753 | C22 | semidirect |
| 23. #15690749 | C22 | semidirect |
| 27. Q32×C97 | C22 | semidirect |
| 93. C2×C97 | #510 | semidirect |
| 98. C97 | C2×#510 | semidirect |
| 103. C2×Q32 | D97 | semidirect |
| 121. Q32 | C2×D97 | semidirect |
| 193. C2 | #20261177 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| C2×Q16×D97 | 2 |
| #20261177 | 2 |
| C2×#15690756 | 2 |
| C2×#15690755 | 2 |
| C2×#15690753 | 2 |
| C2×#15690749 | 2 |
| C2×Q32×C97 | 2 |
| C2×#510 | 97 |