Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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. #10596545 | C2 | semidirect |
| 2. D4×PSU(3,𝔽2) | C2 | semidirect |
| 5. #10593559 | C2 | semidirect |
| 6. #10593559 | C2 | semidirect |
| 7. #10593558 | C2 | semidirect |
| 8. #10593557 | C2 | semidirect |
| 9. #10593537 | C2 | semidirect |
| 10. #10593535 | C2 | semidirect |
| 11. #10593532 | C2 | semidirect |
| 71. C32×D8 | Q8 | semidirect |
| 72. #3753 | Q8 | semidirect |
| 73. #3753 | Q8 | semidirect |
| 74. #3745 | Q8 | semidirect |
| 97. C32×D4 | C2×Q8 | semidirect |
| 101. C4⋊(C3⋊D3) | C2×Q8 | semidirect |
| 105. C32×C8 | C2×Q8 | semidirect |
| 106. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 205. D8 | PSU(3,𝔽2) | semidirect |
| 237. C32 | #3384 | semidirect |
| 249. D4 | C2×PSU(3,𝔽2) | semidirect |
| 266. C8 | C2×PSU(3,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596545 | 2 |
| D4×PSU(3,𝔽2) | 2 |
| #10593778 | 2 |
| D8×#157 | 2 |
| #10593559 | 2 |
| #10593558 | 2 |
| #10593557 | 2 |
| #10593537 | 2 |
| #10593535 | 2 |
| #10593532 | 2 |
| #3384 | 9 |