Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
816 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 258 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 |
|---|---|---|
| 3. C2×#15690873 | C2 | direct (N × H) |
| 11. #15690873 | C22 | direct (N × H) |
| 13. C22×Dic194 | C4 | semidirect |
| 16. C2×Q8×D97 | C4 | semidirect |
| 20. C22×Q8×C97 | C4 | semidirect |
| 32. C2×Dic194 | C2×C4 | semidirect |
| 36. Q8×D97 | C2×C4 | semidirect |
| 47. C2×Q8×C97 | C2×C4 | semidirect |
| 58. Q8×C97 | C22×C4 | semidirect |
| 75. Dic194 | C22×C4 | semidirect |
| 77. C22×C97 | #103 | semidirect |
| 79. C2×D97 | #103 | semidirect |
| 91. C2×C97 | C2×#103 | semidirect |
| 93. D97 | C2×#103 | semidirect |
| 97. C97 | C22×#103 | semidirect |
| 108. C22×Q8 | #87604 | semidirect |
| 129. C2×Q8 | C2×#87604 | semidirect |
| 157. Q8 | C22×#87604 | semidirect |
| 179. C22 | #15690873 | direct (N × H) |
| 191. C2 | C2×#15690873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095519 | 2 |
| C22×C4⋊#87604 | 2 |
| C2×#15690873 | 2 |
| C22×Q8×D97 | 2 |
| C22×#103 | 97 |