Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19150217 | C2 | semidirect |
| 2. C2×C4×Dic349 | C2 | semidirect |
| 3. #26013566 | C2 | direct (N × H) |
| 7. #19150217 | C22 | semidirect |
| 10. C4×Dic349 | C22 | semidirect |
| 13. #41×C349 | C4 | semidirect |
| 15. C2×Q8×C349 | C4 | semidirect |
| 17. C2×D4×C349 | C4 | semidirect |
| 26. Q8×C349 | C2×C4 | semidirect |
| 30. D4×C349 | C2×C4 | semidirect |
| 55. C2×C349 | #104 | semidirect |
| 57. C349 | C2×#104 | semidirect |
| 65. #41 | Dic349 | semidirect |
| 67. C2×Q8 | Dic349 | semidirect |
| 69. C2×D4 | Dic349 | semidirect |
| 81. Q8 | C2×Dic349 | semidirect |
| 85. D4 | C2×Dic349 | semidirect |
| 113. C2 | #26013566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150217 | 2 |
| C2×C4×Dic349 | 2 |
| #26013566 | 2 |
| C2×#41×C349 | 2 |
| C2×#104 | 349 |