Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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. #26012470 | C2 | semidirect |
| 2. #26012398 | C2 | semidirect |
| 3. #26012396 | C2 | semidirect |
| 8. C2×#14583826 | C4 | semidirect |
| 10. #19149679 | C4 | semidirect |
| 12. #19149667 | C4 | semidirect |
| 16. C2×C42×C173 | C4 | semidirect |
| 85. C173 | #2126 | semidirect |
| 100. C2×C42 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012470 | 2 |
| #26012398 | 2 |
| #26012396 | 2 |
| #26012041 | 2 |
| #2126 | 173 |