Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
994 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 331 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×#17986397 | C2 | semidirect |
| 3. #22587927 | C2 | direct (N × H) |
| 4. C2×C82×C71 | C2 | semidirect |
| 9. #17986397 | C22 | semidirect |
| 14. C82×C71 | C22 | semidirect |
| 42. C2×C8×C71 | SD16 | semidirect |
| 58. C8×C71 | C2×SD16 | semidirect |
| 67. C2×C71 | #1705 | semidirect |
| 73. C2×C82 | D71 | semidirect |
| 74. C71 | C2×#1705 | semidirect |
| 84. C82 | C2×D71 | semidirect |
| 110. C2×C8 | #11765854 | semidirect |
| 128. C8 | C2×#11765854 | semidirect |
| 137. C2 | #22587927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986397 | 2 |
| C2×#17986372 | 2 |
| #22587927 | 2 |
| C2×C82×C71 | 2 |
| C2×#1705 | 71 |