Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
786 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 235 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. #22627078 | C2 | semidirect |
| 3. #22627074 | C2 | semidirect |
| 4. C4⋊C4×#10596842 | C2 | semidirect |
| 6. C42×#10596842 | C2 | semidirect |
| 45. #14556586 | C8 | semidirect |
| 46. #14556585 | C8 | semidirect |
| 47. #14556584 | C8 | semidirect |
| 51. #126×C73 | C8 | semidirect |
| 77. C4⋊Dic73 | C2×C8 | semidirect |
| 78. #11924007 | C2×C8 | semidirect |
| 79. #11924007 | C2×C8 | semidirect |
| 83. C4×Dic73 | C2×C8 | semidirect |
| 84. C4⋊C4×C73 | C2×C8 | semidirect |
| 86. C42×C73 | C2×C8 | semidirect |
| 106. #10596842 | #126 | direct (N × H) |
| 144. C73 | C8×#126 | semidirect |
| 171. #126 | #10596842 | direct (N × H) |
| 211. C4⋊C4 | C2×#10596842 | semidirect |
| 223. C42 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627079 | 2 |
| #22627078 | 2 |
| #22627074 | 2 |
| C4⋊C4×#10596842 | 2 |
| C22⋊C4×#10596842 | 2 |
| C42×#10596842 | 2 |
| #126×#64408 | 2 |
| C8×#126 | 73 |