Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15690749 | C2 | semidirect |
| 3. #107×D97 | C2 | semidirect |
| 4. #20260539 | C2 | semidirect |
| 5. #20260537 | C2 | semidirect |
| 6. #20260535 | C2 | semidirect |
| 7. #358×C97 | C2 | semidirect |
| 10. #15690833 | C4 | semidirect |
| 31. D776 | C2×C4 | semidirect |
| 40. Q16×C97 | C2×C4 | semidirect |
| 82. C97 | #2139 | semidirect |
| 87. #358 | D97 | semidirect |
| 113. Q16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| C2×#15690749 | 2 |
| #107×D97 | 2 |
| #20260539 | 2 |
| #20260537 | 2 |
| #20260535 | 2 |
| #358×C97 | 2 |
| #2139 | 97 |