Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
230 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22627061 | C2 | semidirect |
| 3. #22626991 | C2 | semidirect |
| 4. #22626980 | C2 | semidirect |
| 6. #22626951 | C2 | semidirect |
| 42. #14556536 | C8 | semidirect |
| 43. #14556535 | C8 | semidirect |
| 44. #14556534 | C8 | semidirect |
| 46. SD32×C73 | C8 | semidirect |
| 64. Dic292 | C2×C8 | semidirect |
| 69. #11924003 | C2×C8 | semidirect |
| 70. Q16×C73 | C2×C8 | semidirect |
| 72. C16×C73 | C2×C8 | semidirect |
| 121. C73 | #12065 | semidirect |
| 145. SD32 | #10596842 | semidirect |
| 166. Q16 | C2×#10596842 | semidirect |
| 186. C16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627062 | 2 |
| #22627061 | 2 |
| #22626991 | 2 |
| #22626980 | 2 |
| #22626979 | 2 |
| #22626951 | 2 |
| #22626327 | 2 |
| #12065 | 73 |