Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
384 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C269 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C269 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C269 ◁ C2×C42×C269 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #501×C269 | C2 | direct (N × H) |
| 31. C2×C8×C269 | Q8 | semidirect |
| 59. C8×C269 | C2×Q8 | semidirect |
| 71. C2×C269 | #501 | direct (N × H) |
| 75. C269 | C2×#501 | direct (N × H) |
| 76. C2×#501 | C269 | direct (N × H) |
| 79. #501 | C2×C269 | direct (N × H) |
| 107. C2×C8 | Q8×C269 | semidirect |
| 135. C8 | C2×Q8×C269 | semidirect |
| 147. C2 | #501×C269 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Q8×C269 | 2 |
| C2×#125×C269 | 2 |
| #501×C269 | 2 |
| C2×#107×C269 | 2 |
| C2×#106×C269 | 2 |
| C2×#97×C269 | 2 |
| C2×#501 | 269 |