Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 1. C2×#15690843 | C2 | semidirect |
| 3. C2×#15690810 | C2 | semidirect |
| 4. #20261129 | C2 | semidirect |
| 5. #20261115 | C2 | semidirect |
| 6. #20261108 | C2 | semidirect |
| 7. C4×M16×C97 | C2 | semidirect |
| 44. M16×C97 | D4 | semidirect |
| 75. C4×C97 | #137 | semidirect |
| 84. C97 | #3152 | semidirect |
| 91. C4×M16 | D97 | semidirect |
| 124. M16 | D388 | semidirect |
| 161. C4 | #15690843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| #20261285 | 2 |
| C2×#15690810 | 2 |
| #20261129 | 2 |
| #20261115 | 2 |
| #20261108 | 2 |
| C4×M16×C97 | 2 |
| #3152 | 97 |