Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
514 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 97 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. (C2×#10596842)⋊Q8 | C2 | semidirect |
| 3. #22627052 | C2 | semidirect |
| 5. #22626943 | C2 | semidirect |
| 6. #22626938 | C2 | semidirect |
| 78. #14556624 | C8 | semidirect |
| 80. #14556622 | C8 | semidirect |
| 81. #14556621 | C8 | semidirect |
| 86. #137×C73 | C8 | semidirect |
| 130. C2×Dic146 | C2×C8 | semidirect |
| 147. #11924012 | C2×C8 | semidirect |
| 151. C2×Q8×C73 | C2×C8 | semidirect |
| 154. M16×C73 | C2×C8 | semidirect |
| 250. C73 | #8953 | semidirect |
| 283. #137 | #10596842 | semidirect |
| 343. C2×Q8 | C2×#10596842 | semidirect |
| 366. M16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627175 | 2 |
| (C2×#10596842)⋊Q8 | 2 |
| #22627052 | 2 |
| #22627049 | 2 |
| #22626943 | 2 |
| #22626938 | 2 |
| #137×#64408 | 2 |
| #8953 | 73 |