Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 104 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. C4×#14556666 | C2 | semidirect |
| 2. #22625473 | C2 | semidirect |
| 3. #22624891 | C2 | semidirect |
| 4. #22624890 | C2 | semidirect |
| 30. #14556614 | C8 | semidirect |
| 72. D584 | C2×C8 | semidirect |
| 90. Q16×C73 | C2×C8 | semidirect |
| 154. C73 | #11598 | semidirect |
| 218. Q16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556666 | 2 |
| #22625473 | 2 |
| #22624891 | 2 |
| #22624890 | 2 |
| C4×#14556614 | 2 |
| #11598 | 73 |