Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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. Q8×#14524194 | C2 | semidirect |
| 3. #31772697 | C2 | semidirect |
| 4. #31772691 | C2 | semidirect |
| 6. #31772682 | C2 | semidirect |
| 18. #22575825 | C4 | semidirect |
| 19. #22575824 | C4 | semidirect |
| 20. #22575823 | C4 | semidirect |
| 22. SD16×C541 | C4 | semidirect |
| 31. Dic1082 | C2×C4 | semidirect |
| 36. #16864513 | C2×C4 | semidirect |
| 37. Q8×C541 | C2×C4 | semidirect |
| 39. C8×C541 | C2×C4 | semidirect |
| 58. C541 | #440 | semidirect |
| 73. SD16 | #14524194 | semidirect |
| 85. Q8 | C2×#14524194 | semidirect |
| 98. C8 | C2×#14524194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#14524194 | 2 |
| D4×#14524194 | 2 |
| #31772697 | 2 |
| #31772691 | 2 |
| #31772690 | 2 |
| #31772682 | 2 |
| SD16×D541 | 2 |
| #440 | 541 |