Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15690735 | C2 | semidirect |
| 3. C2×#15690734 | C2 | semidirect |
| 4. C2×#15690733 | C2 | semidirect |
| 7. C2×#103×C97 | C2 | semidirect |
| 15. C2×Q8×D97 | C4 | semidirect |
| 87. Q8×C97 | C22⋊C4 | semidirect |
| 118. Dic194 | C22⋊C4 | semidirect |
| 134. C2×D97 | #103 | semidirect |
| 153. C97 | #1787 | semidirect |
| 158. C2×#103 | D97 | semidirect |
| 245. Q8 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D97 | 2 |
| C2×#15690735 | 2 |
| C2×#15690734 | 2 |
| C2×#15690733 | 2 |
| C2×#15690722 | 2 |
| #20260592 | 2 |
| C2×#103×C97 | 2 |
| #1787 | 97 |