Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic254 | C2 | semidirect |
| 2. C22×#14523237 | C2 | semidirect |
| 4. #22550017 | C2 | direct (N × H) |
| 5. C2×#16861134 | C2 | semidirect |
| 6. C2×C22⋊C8×C127 | C2 | semidirect |
| 11. C22×Dic254 | C22 | semidirect |
| 16. C2×#14523237 | C22 | semidirect |
| 21. #16861134 | C22 | semidirect |
| 24. C22⋊C8×C127 | C22 | semidirect |
| 32. C2×Dic254 | D4 | semidirect |
| 62. Dic254 | C2×D4 | semidirect |
| 73. C23×C127 | SD16 | semidirect |
| 89. C22×C127 | C2×SD16 | semidirect |
| 102. C2×C127 | #448 | semidirect |
| 108. C127 | C2×#448 | semidirect |
| 114. C2×C22⋊C8 | D127 | semidirect |
| 132. C22⋊C8 | C2×D127 | semidirect |
| 169. C23 | #14523237 | semidirect |
| 201. C22 | C2×#14523237 | semidirect |
| 211. C2 | #22550017 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic254 | 2 |
| C22×#14523237 | 2 |
| C2×#16861183 | 2 |
| #22550017 | 2 |
| C2×#16861134 | 2 |
| C2×C22⋊C8×C127 | 2 |
| C2×#448 | 127 |