Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1350 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 289 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×D4×#10596842 | C2 | semidirect |
| 2. #22627081 | C2 | semidirect |
| 3. #22627075 | C2 | semidirect |
| 4. C42×#10596842 | C2 | semidirect |
| 24. C4×#10596842 | D4 | semidirect |
| 33. #14556588 | C8 | semidirect |
| 34. #14556587 | C8 | semidirect |
| 36. #127×C73 | C8 | semidirect |
| 53. C2×D292 | C2×C8 | semidirect |
| 54. C2×C22⋊D73 | C2×C8 | semidirect |
| 58. C4×Dic73 | C2×C8 | semidirect |
| 59. C2×D4×C73 | C2×C8 | semidirect |
| 60. C42×C73 | C2×C8 | semidirect |
| 75. #10596842 | #127 | direct (N × H) |
| 94. C4×C73 | C8×D4 | semidirect |
| 95. Dic73 | C8×D4 | semidirect |
| 107. C73 | C8×#127 | semidirect |
| 127. #127 | #10596842 | direct (N × H) |
| 144. C2×D4 | C2×#10596842 | semidirect |
| 162. C42 | C2×#10596842 | semidirect |
| 197. C4 | D4×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10596842 | 2 |
| #22627081 | 2 |
| #22627075 | 2 |
| C42×#10596842 | 2 |
| #127×#64408 | 2 |
| C8×#127 | 73 |