Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 67 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. Q16×#10596842 | C2 | semidirect |
| 3. #22626998 | C2 | semidirect |
| 4. #22626978 | C2 | semidirect |
| 6. C16×#10596842 | C2 | semidirect |
| 42. #14556536 | C8 | semidirect |
| 43. #14556535 | C8 | semidirect |
| 44. #14556534 | C8 | semidirect |
| 46. SD32×C73 | C8 | semidirect |
| 65. Dic292 | C2×C8 | semidirect |
| 70. #11924003 | C2×C8 | semidirect |
| 71. Q16×C73 | C2×C8 | semidirect |
| 73. C16×C73 | C2×C8 | semidirect |
| 85. #10596842 | SD32 | direct (N × H) |
| 124. C73 | C8×SD32 | semidirect |
| 148. SD32 | #10596842 | direct (N × H) |
| 169. Q16 | C2×#10596842 | semidirect |
| 190. C16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#10596842 | 2 |
| D8×#10596842 | 2 |
| #22626998 | 2 |
| #22626978 | 2 |
| #22626977 | 2 |
| C16×#10596842 | 2 |
| SD32×#64408 | 2 |
| C8×SD32 | 73 |